The GSR JRSC won't even fit the Type-R head unless you swap heads. Turbo is the way to go if you want forced induction.

I am really not understanding what you are saying about the compression. Is that the GSR or Type R? Either way, the best way to lower compression is to put lower compression pistons in there. You could half-ass it and put a thicker head gasket on there but ultimately, that isn't a good option since the engine is now prone to as much detonation as before with the higher compression.

I say if you are on a budget, save your money and keep the Type-R stock.