I'm pretty sure that the cat is what is different between the GSR and LS. I think that the LS has a shorter cat and a longer header explaining why the GSR header is too short. I have an LS header on my swap and even that was too short (and different flange position) to meet up with my Civic cat and exhaust.

You could either just get a GSR cat (hoping that the flanges will all meet up) or, just do what I did, and have your exhaust lengthened.

JMO.