POSSIBLE SOLUTION - 

I created different product / service items, each with a different billing rate, e.g., "Hourly (2020)" for my standard hourly rate in 2020 and "Hourly (2021)" for my standard hourly rate going into 2021.

Now, instead of ideally setting rates per client in QuickBooks, I select the proper "Hourly" product / service when creating time entries in the Tsheet app. That allows the two systems to automatically pre-populate the time entries in QuickBooks with the corresponding rates when I upload the time entries in QuickBooks. 

It's a little cumbersome to create different "Hourly" products / services, but now I no longer have to add different rates for each time entry manually.

A HUGE IMPROVEMENT, MUCH MORE EFFICIENT. I wish I had found online guidance more clearly suggesting such an approach.