Why not rethink your pricing table in the short term to temporarily adjust for increased demand? There isn't a way to make everyone happy, but many bulk and economy submissions feel like their cards are being held hostage, which I assume is the majority. Maybe you don't want to do this because it sets a precedent every time there is an influx in submissions and you want to keep your prices stable. However I think there is a way to make it work, and if you are really scaling for the future, then this should only be a one time adjustment. At some point action needs to be taken if you can't hire fast enough and boxes continue to pile up.
PSA has already take action. If it were up to me I would combine Standard/Express and increase the price drastically relative to Bulk/Economy. The combine Bulk/Economy so it's not so easy to cut off other submissions with a little price difference. Then increase prices across the board to be more comparable to PSA. You can still undercut the competition without having insanely cheap prices and overloading your employees.