why can I not be prompted to select from another sleeve I have already purchased and are sitting in my 'golf bag', as it were?
One, you didn't purchase the balls (or anything else), but you purchased a (limited) license to use the items. This includes credits. See the T&Cs.
Two, the "other" balls aren't in your bag but in your inventory. Due to the Rule of Golf "No exchange of golf clubs during a round" our golf bags are locked through a round which includes the balls in this programmed environment. Starter balls and "more of the same" are exceptions.
Thus, we should consider the inventory to be "in our garage" rather than on the course - unavailable during a round.
If there is not a way to do this, I would like to request consideration for this feature to be put into the game.
Rather than that, you might want to use some consideration towards your round planning(?) If it's an important round, you better bring enough balls. If it's not that important, bite the bullet to buy some "from the cart girl" or use Starters or abort the round.