Want to work for a smaller fund, but still want to be "heavy hitter"

Hi guys:

I'm in a situation that I'm sure many of you guys are familiar with/have friends who have gone through - would love your thoughts and advices!
I'm currently at a large fund, but highly bureaucratic. Work is 80% internal impression management, 20% thinking / intellectual. The pro is that it's stable, and has interesitng access to deal flow. The con is that I truly don't feel like myself at work. I am still learning, but don't really feel like I "fit" here.

In looking to lateral, I think for me to be fulfilled and happy, I likely need to work at a smaller organization; however, I see the inherent advantage that AUM size brings in PE business, and was just wondering, is it possbile to go smaller in terms of team size/bureaucracy, while maintaining "impact" (aka, still getting access to interesting deals, ability to execute, pay for advisors, access to top management team, etc.).

I'd love to hear your thoughts on how I can progress with my search, and how I can structure my research process to find the best fit possible...understood it will be a hard task but appreciate the insights!