Using 3-state buffers for multiplexing
3-state buffers are used in computers to multiplex different peripherals onto a common bus.

The problems with underlap aren't as severe as you fear. The capacitance on normal inputs will keep them at the previous logic level, for the few moments before the new driver asserts its output.

The problems that could arise with overlap aren't as severe either. All gates have outputs with a limited drive capability, and can withstand a short circuit for a few moments. Although two outputs fighting to take a bus to different levels could/do take the bus level to an invalid logic level, this will only happen within a tiny time window, and any proper system design would not be trying to read the bus state at that time.