Is the rum still drinkable after being used to boil the boba? If not, aren't you using up a lot of rum doing this?

In any case, my recommendation would be to boil the baba normally, or maybe in a rum/water mixture (maybe 30/70?). Then, after you've boiled them, leave them soaking in rum until you use them. I suspect that the textural difference might be due to the fact that the steam being absorbed is largely alcohol instead of largely water. But, then, I'm no chemist.