Am I stuck forever in this MM PE fund?

I am currently working in a European Middle Market Healthcare specialized fund as a second year analyst, the firm doesn't have the best culture in the street - deliberately slowing down the promotion process (takes 2x time compared to a normal fund to reach to an associate level), numeration level being 20%~30% less to the market average among the similar firms. Joined initially for: a. it's a PE fund (work being more interesting and I was hoping to skip the IB years), b.better work-life balance - the firm is offering to relocate to the NY office for a year this coming September, c. the people I worked with was amazing. However as the firm has grown nearly 2 times bigger (in teams of size / AUM) over the past 1 year (promotion opportunities even rarer), plus the fact that I have stayed long enough to really learn what this firm could offer, I am wondering how I should plan my next steps? I tried networking with the mega funds but it seems that my profile isn't super interesting. What can I do to get out of this sort of stagnant situation? Any word of advise is much appreciated