I think DX sku 22934 is probably the best thrower for under $50. It is the recoil thrower. It has a larger head/reflector that the P60 lights and it is a recoil design (meaning the led is attached to the front lens and points back at the reflector.
I don't have it so I can't say for sure. It depends on how hard the emitter is driven. The R2 drop-in from DX is supposed to be driven pretty hard I believe so that in a P60 host even with the smaller head might be just as good but I don't know.
To answer the question about using an aspheric lens. In the case of a P60 host, L2, P6, or whatever, the 28 mm aspheric lens from DX is used to replace the front glass lens in those lights. Supposedly this puts it at the correct focusing point. I can't say for sure. I have those parts on order but haven't received them yet.
DX sku 16538 might be better. It uses a R2 and a 50 mm reflector. My guess is this one probably throws the best for an under $50 light. It's around $25 actually.