I am trying to take convexity adjustments into account in the bootstrap on the SOFR curve.

I am using cash for the upfront, SOFR swaps from 2Y to the end.

In the mid term I use 2 1M SOFR futures and 7 3M SOFR futures.

For each of the 9 futures I want to calibrate a simple model (Ho-Lee or maybe Vasicek) to on a small implied vol surface to price the convexity. What is the market practice ?

These american options I have to calibration the model on are all american options (and not european options as because of the collateral an early exercice could be optimal) so that I don't know which model is the best fit regarding this task, as american option should be priced really quick as they will be be used for calibration. Ho-Lee or Hull-White + tree pricer or pde pricer ?