Non-shorting SPDT switch using MOSFETs

My goal is to design a circuit using MOSFETs that would switch 12V power to one of the two high-current loads, using high-side switching. Control is done by a 3.3V MCU. The reason for using MOSFETS is to keep the size down.

This is my current design. The problem is that there’s a short period when both of the MOSFETs are on.

One obvious solution would be to separate the control of the circuits so that both could be turned off before switching between the loads. The downside being that the responsibility for keeping the loads from being turned on at the same time shifts to software.

I’ve looked into using gate drivers, but unless I’m missing something, there doesn’t seem to be a driver for a pair of P-MOSFETS which is what I think I need to be using for high-side switching.