PE recruiting from mid-tier RX

So I am starting FT at a mid-tier RX group and I want to recruit for buyside, but I don't really have a strong interest in pursuing distressed / special situations as a career. I would prefer to recruit for traditional UMM/MF PE, but I am really open to any reputable MM firms. I realize that buyout exits are pretty common from top RX groups, but can the same be said for the mid-tier groups? Given my background, I guess I am open to distressed funds with a control strategy such as KPS, but would eventually look to move to traditional buyout.

I am also curious about the interactions with headhunters. Do headhunters try to push you towards distressed / special sits opportunities, or are they open to showing you opportunities in buyout if you tell them that is what you are interested in? Do special situation groups use the same set of headhunters and timelines as traditional PE?

I am also a little concerned about ruling out special sits since I know that is where I would have the most opportunities and I am not in a top group. I have heard that it is best to be precise with what you want when taking to headhunters, but would it be ok if I told them I would prefer a fund with a control strategy, but I am also open to Special Sits just in case normal PE does not work out?

Would appreciate any insight into what the process looks like and the best way to go about it.