Thinking our loud here.... What if the cupholders were attached/inserted via a pair of dowels rather than a slot?
Then you could drill pairs of holes of that diameter at various intervals around the table.
Would probably want to use oak or a similarly strong wood.
Whichever solution you settle upon, I would be mindful that any bracket/block added to the underside of the table will reduce leg space (thigh space, to be exact). I’m not a giant — just a little over 6' — but a pet peeve is when the top of my bent leg jostles the underside of a table.