Just set the maximum number of rebuys per-player to 1. Then the Rebuy dialog will only list players who are eligible (who haven't yet rebought). Once the break arrives, change the Bounty Chip Cost to 0 (meaning no bounty chip) so all rebuys after that point will omit the bounty chip.
What you should be able to do is simply rebuy a remaining player, including a bounty chip, and they should "keep" their original bounty chip (since no one knocked them out). I just checked and this is not how the software handles it. When you rebuy a player who hasn't busted out, effectively the initial bounty chip goes no where, as far as the software is concerned. The player never surrenders it to anyone and so it shows as a cost, but no one collects that fee as would happen if the player surrendered the chip to a hitman or they "kept" it. I've made a note to fix this in a future version.
I would agree, however, that the rebuy for the players remaining who haven't busted out is really an add-on, but it's all just semantics. If you'd rather keep it straight by having it all be rebuys, then you should work your tournament that way. The Add-on and Rebuy dialogs do list the number off add-ons and rebuys each player has currently purchased, so you can always just eyeball it right there in the dialog while you're rebuying players to make sure the player hasn't already rebought. Or, if you wanted to make it an add-on, same rule applies. Just make sure the player doesn't already have a rebuy.