For this: "In the past I’ve entered open invoices using 12/31 charging to opening balance equity"

Your Fee items will not be reported as income when the payment is applied. You can put on the invoice the original historic date and the real charge items.

For Balance Sheet: "and some reimbursed costs" = those are Not Expense. You post that to Advanced Costs as Other Current Asset. If there is a Nominal Deposit to Trust Bank, the Firm's money in Trust Bank their money still as asset.

We already covered the Settlement question. It helps to keep to One Subject and not "cross-post" the same issue in Lots of topics.