Networking / Cold Recruiting

Hey All - as the title says, I am looking for some advice on networking to hopefully be able to move from IB to a L/S Hedge Fund. I've been in touch with some recruiters, but haven't gotten many actionable leads, so I was planning to start doing some networking on my own to help with the process. I've read a lot of helpful threads here already, but I thought it could be worthwhile to ask a few additional questions that I'm trying to iron out before I start.

My main questions are:

1) My main plan of outreach was to leverage LinkedIn and use a relatively short message quickly introducing myself and my interest in the HF industry, mentioning why their fund in particular was interesting, and then requesting time to chat. I also plan to include one / two quick stock pitches since I've heard that advice on this forum before, but did not know if I should be more expansive in my initial email?

2) I was planning to frame my interest in terms of an informational interview / desire to break into the industry and then see where the conversation goes, but did not know if I should be more direct in terms of discussing job opportunities? 

3) Is there any reason to only target funds above a certain size (AUM or employees) or since response rates will likely be low and opportunities could come from less likely places, I should be trying to network with as many people as possible? I was leaning towards trying to talk to as many people as possible, but did not know if my energy would be better served elsewhere