Maximizing Chances at Long-Term PE Career

Hi monkeys. I started a few months ago as an ASO at a LMM/MM firm that will likely be a 2-3 year program before I am pushed out. The firm is relatively reputable given the fund size, and I am enjoying the work. As I think about making the transition to Senior Associate and eventually VP, would it be better to try and lateral after my time is up, or is it worth considering an MBA? A small number of former associates at the firm have made it to H/W, though I'm an overrepresented male so might be targeting more Booth/Columbia assuming I score as expected on the GMAT. I've seen conflicting info on this site with regards to getting an MBA, with some threads saying it is the best way to move upmarket (maybe only true for HSW?) and some saying people end up moving downmarket anyways, similar to many laterals. Assuming I would like to either move upmarket or stay around my current fund size ($1BN), is it worth considering the MBA if it's a non-HSW M7, or even T15?