Which to pick based on described needs

it’s not.
But, I would suggest you look for an alternative.

It doesn’t matter what frequency you use for this, so just replace the 125kHz xEM Access Controller with a 13.56MHz alternative.

You have a number of choices.
You could buy off the shelf the HF equivalent of the xAC, like this.

https://a.aliexpress.com/_mP84VUU

OR

If you are familiar with arduino, then you could make your own

OR

A community member project