How heavy is your cardstock? Adding a cardboard core also might be causing more issues for you, because it can cause the paper to flex to a different shape than the original design. I used heavy cardstock on all of my paper builds, and also a quality glue gun. The cheaper (and often small) low-temp glue guns really limit your seam strength if you try and run longer sections in one pass, multi/temp or high-temp guns give more wiggle-room.
Styrene and plastic welding could work, I guess I would be concerned with complex intersections where several pieces come together at different angles; if you accidently weld one angle a few degrees off (which would likely be hard not to ever do with pepakura) then your next connected piece might have to be flexed/trimmed/compensated to fit, if that makes sense. Just my two cents anyways, good luck with it!
