Reconciling income that posts the following months

I use a different cloud solution than Quickbooks to handle invoicing (it's part of a healthcare solution that integrates scheduling, charting, payments, etc).  I create invoices and accept payments the same day in the solution, and then it trickles into my bank account, and finally is imported into Quickbooks as the bank is linked.  I categorize the money that flows in as income.  Where I'm struggling is that when I try to reconcile, those transactions in which payment is received at the end of the month in the health care solution do not make their way into Quickbooks until about 2-3 days later, into the next Month.  So I generate a report in the health care solution, and it shows $1000 earned income in the month of January, but because monies earned at the end of the month post in February, my reports don't line up...Quickbooks says, for example, $900 in the month of January because a $100 check cleared into the next month.  I thought of changing the dates on the transactions in QuickBooks to match, but I have a feeling that's a really bad idea, as Quickbooks then fails to match with my bank.  While I'm sure this may not be a big deal in the accounting world, this issue makes it a pain in the neck to make sure everything lines up.  Wasn't sure how most people handle this discrepancy.  Does anyone do anything with tagging the transactions for a particular month...just not sure the best route to go here.  What makes this even more of a hassle is that all of the transactions are the exact same amount, so it's tricky sometimes to understand what monies came from what month.