Invoices are backdated to the time when the transaction historically happened, but payments dates are dated to the time we create the transaction in Retail. 
We create this payment with a special type, called “Historical Payment.” This payment type is initially archived, but can be unarchived in the Settings > Payment Types menu.
To deal with the sudden surge in historical payments, you can go in the Reports > Payments > Received menu, and:
Generate reports for all other payment types individually.
Create a report for the Historical Payment type, and subtract it from their other reports. 
There are no other ways for Lightspeed Retail to overcome this potential accounting burden.