Will this set work with 2 inch squares?
I use my 1.6" sets on my 2.25 board because I didn't want to buy a 2.125 board to match. It took a little bit to adjust to it but now I like the roominess. You might be able to adjust your preference to a 1.6" king on a 2" board too. It is worth a try for $60.
Those king base 'rules' are only true for most Staunton sets. I noticed that some Soviet replica's the king base is almost the same base as the rook/knight. And the difference in base diameter between the pawn and the rest of the pieces is much smaller. There is even a set where all the pieces have the same base! So I wouldn't trust these guidelines blindly.


The description recommends 2 - 2.25 inch board. King height 3.75 and base 1.61 inch. It should be fine, maybe slightly crowded on a 2 inch but fine for casual play, right? I just don't like them too crowded.
https://www.chessbazaar.com/offers-zone/clearance-sale/the-cb-grandmaster-staunton-series-chess-pieces-3-75-king.html