Nice suggestions from both of you. Thanks!
@caver01 There IS a recess/gap of about 2 cm, so you idea about a square piece of wood that fits the inside of the edges is quite brilliant. And would be very, very easy for me to do. It would be steady from sliding to the sides at least, and I can probably attach something on the back and/or front, so that is also keeps it from sliding back and forth.
The best part of that idea is almost that the recess/gap was probably going to look a bit strange on the stand (because the bartop bottom can't be flat on the stand), but this solution can actually hide that gap when it's on the stand, making it look more like a full size cap!