Capt, looks like you got some great responses! I think everyone made great points. Your self-analysis was spot-on as well.
As you said there are a number of little things going on but the biggest thing in overcoming the "under 100ft barrier" in cast distance will come from focusing all that energy you are putting into the blank into a smaller, straighter cylinder with your forward stroke verses spreading it over a wide circular shape.
Breaking down the forward cast, I would choose 3 things: (a) the path of acceleration
and (b) application of power
and (c) hard abrupt stop
to think about first and foremost to 'break the barrier'. I have some recommendations for correction, but first let's do the analysis:
A) Path of acceleration:
Specifically, the line's path in your sample clip drives upward at about 25 degrees above horizontal, while the final stop of the rod forcefully directs it below the horizontal to finish. This means that the energy pushes in two opposite directions - upward leading up to the stop; and downward after. This will inevitably open the loop. You can actually see the conflict of loop energy in the loop shape in slo mo.
In the gif animation I made (below), I took several snapshots and drew over the line as it appeared in the snapshots. You can see that the path of accelertion initally drives the path of the line upward (orange arrow up).
Then as the arms release the power the deflection creates a large circular shape and the energy from the tip drives the path abruptly downward (orange arrow down).
These arrows must be kept horizontal and in-line, and the acceleration must increase from start to finish before the stop.
The green horizontal line in the last frame is the path represents how the line should track in order to maximize the energy of the rod flex into the cast itself. It can be lower e.g. sidearm as long as it tracks true.
Practice with the smoothest, least energetic stroke possible that tracks the line properly. Don't worry about power or distance first, get the tracking and smooth acceleration down first instead. Power and distance are easy to add to good form, however the inverse is not true.
Also keep in mind that we can't see the birds-eye view here. The operative part of the loop must track in the same line in the other dimension as well, that is to say that bird would see a straight path as well if it flew overhead.
B & C) Application of Power and abrupt stop
Try to influence the line with the rod such that the line maintains tension from tip to fly in a horizontal "lane", then stop the rod as close as you can to that path so the energy remains focused, resulting in a tight an powerful loop.
Note that the distance between the rods stop point and the path of acceleration (which must be straight) equals the size of the loop, per Bruce Richards.
It's clear that you are getting a lot of energy to load into the rod; and the IM8 graphite although flexible will recoil and dampen quickly - however the influence of this energy on the line seems a bit unsteady. I suspect it has something to do with turbulence in the line we can't see during the backcast, in other words it wasn't straight at the start of the foreward cast (?).
In any case the rod is flexed quite hard early in the stroke and unloads well past the optimum stop point (with a large deflection). The final rod stop is nearly horizontal verses close to the ideal path. In summary, too much power at the end of the stroke, the tip looks as if it might be getting driven down with the bottom hand well past the ideal stop point, possibly.
In an actual class environment I would work from a selection of mnemonic devices based on feedback from you (interactively) - but in general terms here is what I would prescribe as a starting point...
1) Get things straight, first and foremost
Your goal is to track the line in a straight horizontal path. Learn to identify with the way the rod and line interact; that is to say strive to really feel how the rod makes the line glide smoothly and within a horizontal imaginary cylinder. Don't worry about distance at first, just think about smooth / straight tracking of the line.
Key tip: In addition to straightness, the line must be moving slightly faster in the front than at the back at all times, in other words there must be tension from end to end. This tension helps keep the line stable and easier to steer. It does not take a lot of power, just acceleration. Do it lightly and slowly at first to really feel the pull that makes things stable. Use that stability to keep the line horizontal.
Move your hands and arms properly. An example of a mnemonic I often use while teaching is the 'knuckle dragger'. In your hallway, place your knuckles on the wall about where your upper hand would be, about eye or ear level. Stand at a comfortable distance and while keeping your knuckles touching the wall make the longest forward and backward stroke you possibly can while keeping your knuckles touching the wall on a perfectly horizontal line. Move your hips, legs, shoulders, arms, etc to accomodate this 'straight rub'. Do this at full casting speed, without your knuckles leaving the wall. That shows you exactly what your body needs to do when casting. It will also prove beyond any shadow of a doubt to your family that you are in fact, nuts.
Now with the bottom hand, grab the shirt sleeve of the other arm along the bottom of your bicep near the elbow. Make these casting motions again, holding the shirt sleeve with your bottom hand so it never rises above your other elbow. This is what your hands need to be doing, moving in concert while maintaining the proper angle to load and unload the rod through the stroke.
2) Application of power
Once you get things tracking well, it only takes a small adjustment in technique to break the 100+ft barrier. When a cast is done well, you don't have to hit it hard to make it go. Take the well-formed cast and add just a little bit to it and it will likely go as far as your hardest hit cast ever went.
Keys to distance: extend and accelerate
Get things tracking right, then extend the path length and increase the total rate of acceleration before the stop. Path and rate of acceleration go hand in hand, because the longer you can make the path, the more potential you have to accelerate. Extend the length of the stroke by adding drifting reach to the end of the backcast and going for as much change in speed (not speed but change of speed) from start to stop.
Bottom hand power:
Although the bottom hand assists through the various parts of the casting sequence, it's only real power moves are (1) a subtle kick out to form the backcast and (2) a fierce inward tuck to finish the forward cast in place of the single haul.
It doesn't take much to make a good basic cast go really far. However it takes a lot of energy for a cast that tracks offline to go half as far.
3) hard stop!
Lastly, make the stroke much more compact so it stops near the 'green line' in the gif, keeping the energy very focused. Do not apply a big whammy at the end, instead get the rod loaded as you have and put on the brakes suddenly instead.
Imagine a catapault with a rock in it. The rope is cut, and the load is springing back fast. The harder and more abruptly the shaft hits the block, the more of a line drive you get.
Choose the right practice line. Using too short of a belly or too dense of a material gives you a 'jumpy' feeling you don't want while tuning. You are trying to identify with smoothness and straight line path stability.
It's fine to practice with shooting heads but get them at least 35'-38' or longer. For pure casting joy the 50ft plus heads are awesome however in fishing involving strip retrieves and fish that hit close to shore that's a lot of head to fish with. An appropriate line to practice with loads the rod sufficiently yet does not overload or deliver a choppy feel. It's good to practice with head lengths that are realistic for your fishing applications, but not advisable to start with super high-density heads. Use a floater or intermediate or lower density sinking line to get the feel as described above, then try the higher density lines as fishing situations dictate.
Film yourself again until the black lines are moving parrallel to the ground and not getting ahead of itself or the rod. S-m-o-o-t-h. I use video analysis a lot, both when teaching classes and when working on improving my own technique.
Thanks for providing this opportunity to those of us who enjoy the analysis, and also for providing some fodder for the benefit of others who are interested in the topic.