I mostly use Dunlop Trigger spring-loaded capos, or the original Shubb. I don't have this problem, and most of my guitars are 1-3/4" necks - or even wider in the case of my Seagull S6. I've also tried most every common capo out there, but Trigger and Shubb are my go-to options.
A classical capo will likely not work all that well, being designed for a flat finger board. Maybe try a capo specifically intended for a twelve string guitar. Twelvers are 1-7/8" necks typically, and that would give ou plenty of width to work with.