Does it make sense to go from software CD->traditional PE if my end goal is software PE?

2nd year corp dev analyst covering several software verticals. LT goal is to get to a MM+ software buyout shop, expecting to probably shoot for an MBA. Have an opportunity to lateral in my non-T1 city to a LMM shop that's more traditional (manufacturing, business services, transportation) with a $250M-500M fund. GPs look solid, there would be a decent pay bump, and I'd get more of an execution experience in a principal investing role vs the sourcing & execution-lite role I'm in now.

Does it make more sense to pass on this and wait until an opportunity to jump to TMT banking/software PE so I can stay in my sector or is it reasonable to get the principal investing experience first even if it's not in the same vertical I know I want to get to LT?