If they don’t have business, they won’t have finance. Econ is a social science - think history, poli sci - yes, more numbers but it’s not finance.
F&M will be a reach but has a business major.
Gettysburg a target. Also has a business major although these may be more generalist than finance.
As you have unlimited funds to pay, this will give you an edge at some schools as they are need aware and love full pay.
With recruiting though, it’s more about who will want you - and where will you qualify. If the Lafayette coach said no, but Hobart said yes, wouldn’t you then look there?
You mentioned Swat - I don’t see a way for you to get in there- but perhaps a coach has pull, as an example.