I used this from Amazon thinking that 1” dots would cover all the base of my pawns and most of the base of the major pieces. King 4.0”. Works great. I tried dots that were .75” before but those didn’t work.
https://www.amazon.com/dp/B007Y7DKWC?psc=1&ref=ppx_yo2_dt_b_product_details



Original Centaur left, FIDES World Chess set rightI have also discovered that the FIDES style plastic pieces from the World Chess starter set also seem to work well out of the box with little mod.
Now that's a suitable upgrade.