To edit Account Team Members, you need Read/Edit on Accounts. If you were to create a sharing rule, you can open up access. We use the "Type" field to designate Customer vs. Prospect, so i would use the criteria below.
Type equals Customer
Assess with Account Sharing Rule
Contact As you see fit
Opportunity As you see fit
Case As you see fit
If you are not looking to use the field, or if you still need the Group to have access no matter what if there is a won opportunity, you can create a Rollup field on the Account that does a count of Won Opportunities, and share via a Sharing Rule again, if the value is >= 1.
You can find Sharing Rules in Setup - Security Contols - Sharing Settings.
Please make sure their Profile has Read/Edit permissions on Accounts also.