Indicating an interest in a specific PE fund strategy to HH

I wanted to see if any other monkeys had any insight into how to go about communicating an interest in a strategy to HH for the on-cycle recruiting process for PE. Elsewhere on this forum, people have mentioned it's really important to be clear about what you want in the on-cycle PE process. How important is it to be specific about strategy within private equity (and even within specifically buyout strategies) when talking to the HHs? I'm interested primarily in the UMM/MF space, but within that there's definitely some variation within how the shops in that space pursue assets. For example, one could say they are interested in a more value-oriented approach that doesn't shy away from hairier, stressed/distressed situations and another strategy may be focused on buying industry leaders and focusing on a growth thesis.

Is this something that an analyst should have a great grasp on and communicate to a headhunter? Doing so would seem to limit the types of opportunities that a HH would want to send your way since if you were to indicate the former, that would perhaps preclude you from interviews at funds such as H&F, KKR, or Bain (just spitballing - not trying to say this is what those firms definitively do) that are more willing to pay up for what they view is a good business. To take one step back, it seems a bit premature to make such a judgement that early on in a banking stint anyway, so do headhunters even take that kind of statement seriously at all? Really appreciate any insight into this. Any advice on how to best communicate interests generally is also helpful.