I’m guessing I’ll have to go to search investors give them ROFR on the deal to raise for the search but also IS capital providers to finish the raise but still working on the details.

Loving this thread!
On the initial question, I think a roll-up strategy will likely resonate more strongly with PE than with Search backers imho. From what I can tell, the cap. table with search tends to be an inch deep and a mile wide - tough to generate a strong current in those waters.
On the PE front, and I've seen this a couple times, your plan reminds me of an EIR or CEO-in-residence wherein you're backed by the firm to lead the roll-up. I would agree with other posters that this would likely entail a hands-on approach. As much as your current gig isn't immersed in ops, I would expect you to be (or become) the expert on the sector in order to back the enterprise. You'll need help, so networking to a strong COO is key.
Thinking about my own background, I appreciate your perspective - I've been in financial services 'arm-chair quarterbacking' commercial banking clients and prospects for close to 15 years. Recently, I've been trying to get back in touch with a former self of mine who worked for almost ten years in industry accounting roles (mostly but not exclusively tech). Living and breathing the weekly, monthly, quarterly, annual universe of a single business - haha, that's actually what led me away from industry into financial services back in the day. But might be time to go back. My advice, no half measures.