The way (multi-table) HORSE tournaments are generally played is to have levels of a fixed length and play a fixed number of hands of each game - often equal to the maximum number of players which can be seated at a table, say 8.
Say, you decide on playing a 30 minute levels. You would play 8 hands of holdem, 8 hands of omaha, 8 hands of razz, etc. in order. When the 30 minutes elapses, you would just raise the blinds and antes and continue with the rotation of games.