I have not found a solution. The previously mentioned link was helpful to get the check number to show up on the reconciliation widget. I can visually match and reconcile it this way. While this works, it is not only manual but cumbersome. I can sort the transactions in Odoo's widget so all the check numbers are together. I could also filter the transactions as well. However, once I validate a line, whatever sorting/filtering I've done gets wiped away and returns to a default view. I can't modify the widget through Studio so I guess I'm out of luck.

What seems to be lacking is a way to use a reconciliation model to detect the check number from the bank statement line (in our case it is part of the bank's label/description rather than a separate field) and match it with the recorded payment in Odoo. I would think this would be important to many US based customers. It seems like the reconciliation model has the capability of this, but I haven't had any luck in figuring it out.