You’re overthinking it. There’s a pretty small difference between 2.1 and 2.2. You could swap between two of the same tire but in different materials and have a greater difference in rolling resistance than swapping between a similar 2.1 and 2.2 tire.
The fastest option is just to put slicks on, but i don’t think that’s really necessary. I’ve done a bunch of tarmac rides on my XC tires, it works just fine.