Okay so here are my thoughts with the updated info I got.
Regarding special moves, the GIF on Seiya's page might somewhat disagree with you Matt. As the move describes, Seiya first uses his hands to trace the Pegasus constellation and burn his cosmos until he reaches his peak of power. Of course it won't take too long, but that does show it takes a few moments to perform the move. This would give Storm Pegasus a chance to attack him before he unleashes Ryusei Ken. But for arguments sake, we can say Seiya unleashes immediately enough. Pegasus, in its beyblade form, already has a good size advantage to make it harder for Seiya to physically hit it. And regarding speed equalized, for now i'll ask why wouldnt that make Pegasus's speed the same as Seiya's punches? In speed equal battles, everything speed related is supposed to be effected down to the core. With that, I don't see why Pegasus would overall have trouble dodging or avoiding Seiya's physical attacks.
Next, reality wariping. I don't deny Saints being able to escape pocket dimensions at all, but that wasn't the intent of my point here. What I was saying is Pegasus's incomplete Storm Bringer by itself has the effects of not only heat energy + soul destruction, but also reality warping, which can warp a pocket space into a universe. Basically, my point here is this regular attack in itself has 3 simutaneous effects all in one that Seiya would be hit and forced to deal with.
Finally, i'll ask this again. I know Seiya's basic stuff like atomic destruction, but would he be willing to do that early against...well....a spinning top? Im not saying Seiya wouldn't start off with it, but the thing we need factored in here is Seiya's opponent. A teenager with a crazy haircut owning a toy. The likelyhood of Seiya underestimating Pegasus as a joke is very high, which would give Pegasus an opportunity to do something major before Seiya starts taking it seriously.
I have more but i'll wait on it.