This part makes no sense: "just consolidated all the open invoices to 4 main open ones and she closed the rest with credit memos...."

She closed out old sales as a write off, then made a New Sale?

"now the payments are coming in against ar, depositing positively in the bank account, but not going toward any particular invoices. Is that right?"

Never; if there is an open balance you apply it. If there is no open balance, then stop using Receive Payment. That is an AR activity. You never want Negative AR; that is Backwards.

"It shows the deposits as positive to the bank account but negative in the client sales screen"

Because you "received Money and I don't know why they paid you, since they don't seem to owe me."

This is why you use Sales Receipt, instead of Receive Payment.

But you stated there is one Combined Invoice, so which is it? Did they have an open balance or not? Did the Credit Memos use an item that "closed" out the unpaid sales to a different Asset account? You have to look and understand the conditions that exist.