Scratch my previous post on this, this is the right way to do it.
The easy way to have multiple tycoons at once with several different players is just to have the brick ownership changed to the player of one of the tycoons, probably with the player "buying" it, and with all bricks under that tycoon's baseplate becoming owned by them (this is fine as long as they can't modify the bricks as in building and painting are disabled). That'd allow for all of the bricks of have different names and still run normally. This is assuming no one has eachother's trust, since that allows players to work together on one or two tycoons at once.
I didn't test this, since I can't test this right via a LAN server or internet game right now, but it should work fine.