Oof, I would at least go for a 4k Sony. In hindsight I didn't think the hw40es was really that good of a projector.I’ve considered picking up a Sony 45es strictly to game on. 16-22 ms is pretty decent.
It would save some life on the JVC and I could leave the JVC set for 2.40 and Sony pillarboxed for 16:9 gaming.
But if games input lag are that important to you. You should really wait for the upcoming Nvidia BFG series which were made specifically with this in mind. 10ms input lag running on 4k with NATIVE 120hz and gsync , very interesting specs.