If you have a tank toilet you might be able to adjust the floater (bend the rod upwards) so it never quite turns off the supply valve. Failing that, you can just manually prop the flap open with something.
If you have a flushometer, remove the nut over the valve and adjust the screw underneath until the valve never quite shuts off.
Warning: Take careful note of exactly how things were before. A toilet that never stops running can be just as hard on the spirit as a toilet that doesn't work at all.
Alternatively, why doesn't the grinder have a higher minimum triggering flow rate? It seems it's falsely detecting potential solids arrival.
Trickling your faucets (just a drip-drip-drip) for a few days is a small amount of extra wear on your pump in exchange for not rupturing pipes.
It sounds like the answer is that to be effective, you'd have to put too many of them along the length of the pipework.
(Edit: Houston only.)
[1] https://www.wfaa.com/article/weather/if-dripping-faucets-sav...