Using incrementing ballot numbers is fine. If you have multiple Proposers all sending the same ballot number in Phase 1 (Prepare & Promise) the Acceptors will reject any ballot number less than the highest ballot number they have received. In order to move to Phase 2, the Proposer needs to receive the thumbs up from a majority of the Acceptors, which means only one Proposer can ever win.
If you were to divide the ballot number space, in the event that the owner of the highest values in that space won, every other proposer would immediately need to increase their ballot numbers for all future rounds and so on and so forth or else they would always get rejected.
If you were to divide the ballot number space, in the event that the owner of the highest values in that space won, every other proposer would immediately need to increase their ballot numbers for all future rounds and so on and so forth or else they would always get rejected.