You’d score in the Big East but you weren’t a recruited athlete at your current school?
Anyway, yes coaches at Georgetown probably can get you in (if they want to) but you need to ask them specific questions about the process. I’m not sure how specific they can be given transfer portal rules and the various windows but they should be able to lead you in the right direction.
No idea about Davidson or Colgate. I’d have a direct conversation and ask the coaches, but if they said to get an application in I’d do it asap.
This isn’t a typical situation, even with the transfer portal. If these programs are looking for athletes in the portal they probably had most of those conversations back in the fall.