There is no reason to wait and decide on a school, post acceptance letter, if you know that attendance is a no go because of cost. Better to focus on those programs which are affordable; and I would strongly encourage you to consider D2 schools with strong academics as they can package scholarships to include athletic money. NCAA Division III has the greatest emphasis on academics, but there are many D2 or NAIA schools which also allow for a healthy balance between academics and athletics; and these schools may well be more affordable.
NCAA Division III schools can have large rosters because of the philosophy of the department/school - Athletics is a component of the collegiate experience, not the focus as in DI and some DII programs. Because of this, D3's tend to have large/inclusive rosters open to a wide range of talents. How this affects playing time depends on the coach and the department. Some will accept many on to the the team, but only the top 8 will play while others have a stance of everyone plays if they are on the team.
I will close by encouraging you to communicate with the coach of your upcoming D3 visit, but to also stay active in your outreach to other programs so you have options.