You've made it pretty clear that you are interested in overhead casting with two-hands, but yes there is carry over between all of the styles to an extent. Even with the single hand rod any known spey casts will be used regularly as opportunites present themselves.
Two-handed overhead casting is a much different course of study than Spey casting proper, and is often just a matter of adding a dose of discipline to what you already know for eye-popping returns on that investment.
Single handed casting allows a large degree of freedom where bad habits are not very apparent. Two-handed casting requires proper application of power, truer path and a high strong stop to send the line sailing much further with mininal effort but there is a learning curve. BTW once you get it your single handed casting improves dramatically since the same concepts apply.
Spey casting on the other hand is a whole different means of generating energy with a rod and line and it's very easy to develop bad habits while hacking out casts on your own. I should know
I started out working real hard to figure it out on my own, got some helpful instruction from friends, but over the first three years the biggest challenge was to overcome the bad habits I established starting out. 15 or so years later I've cleaned it up a lot, but I remember what a revelation it was to get some direct advice from Simon Gawesworth, Ian Gordon, Mike Kinney, the Carron boys, Nobuo and Tak, or the no-name hardcore spey casters you'd meet out west by happenstance and end up exchanging ideas about casting technique with when the fish were down.
The mechanics of efficient Spey casting are best learned from an interactive observer, meaning an experienced instructor. Video and books all may offer some component of your learning curve that is important as well.
But keep in mind that much of what an instructor can teach you in person is contrary to what you teach yourself. If not, great. But if you have a lot of muscle memory to fight, well not so great.
An instructor with an experienced eye can see quickly what you are doing or not doing and will help you recognize tendencies that you yourself would have a very hard time detecting, never mind correcting. And the more muscle memory you establish the harder it will be to change it later when you get good solid instruction.
Even if the class is only a day long you should walk away knowing that you over-rotated on that cast or that you trunked the bottom hand right then, etc. If you can't recognize what you did wrong from cast to cast then you will be establishing habits that become increasingly difficult to eliminate over time.
Anyway some of the keys to overhead casting rods like the rod formerly known as the Atlantis are path of acceleration, proper application of power with both hands, and where to stop the rod (read: higher).
But the best thing you can do IMHO is get interactive feedback to observe and transition you from what you are currently doing into an effective and efficient two-handed cast technique.