The way I thought about it was to ask what happens if you just have a coin going around a point, which would be the natural end point of reducing the size of the second coin. That of course would give you 1, so a good first hypothesis is that the total is just however many spins the two coins go, plus 1.
The video demonstrates the 1:1 coin size case and speaks about the curvature of the line it rolls on, but your thought experiment makes it a lot clearer. As the size of the other coin goes to 0, the amount "gnawed off" of the rolling coin will also go to 0 while obviously still rotating a full revolution.
