Flyfisha1: you are trolling for the holy grail of a v.long distance casting with a fly rod.
You found greater distance casting using an "off vertical" forward stroke, which you characterized as side armed. The world's experts agree with you.
The absolute authority and master of single hand casting, Joan
Wulff, uses a position named "off vertical" for making far far casts.
The off vertical positions opens your body to allow a full backstroke followed by a maximum length forward cast. The off vertical position keeps the line from hitting itself as well as offering the physical opportunity to propel the fly line the maximum distance because an open stance gives the caster a far great distance to cast.
I attended a Simon G class two years ago when he announced that "flat is good." Simon meant that keeping the forwared stroke flat, as opposed to vertical, a superior loop form will emerge, and an open stance made the flat stroke easier.
Dr. Way Yin and Mr. Steve Choate, world champions in 2003 in England, both use an open position [named "off vertical'] that gives them maximum forward and aft stroke distance, thus delivering maximum energy to the line. Again, Way and Steve make their casts by opening their body for a maximum cast effort.
It sounds like your observational skills will quickly lead you to expert level skill quickly.
Good luck, Bob P