If you shut off the water supply, you will need to open a faucet somewhere to vent the system.
I tried that, no dice. Will try again today, or disconnect the hot water outlet to let it vent.
The pressure in the shower did seem a lot better today, so what I did yesterday may have helped. Pretty sure it's not just a gunked up shower head because 1) low pressure in two separate showers and 2) the pressure is low out of the bathtub spigot as well. But, it was better today, so we'll see.