Turning off water to toilets won't make any difference in your shower. Thinking thru this: What's the difference between the toilet itself shutting of water when the tank is full vs turning off the supply to the toilet? NOTHING! So that's not the source of your problem.
What sort of water heater do you have? Tank type? Is there expansion tank somewhere near the WH? The reason I ask this is in a home my son was living in, the water company replaced the meter and added check valves to prevent back-flow. He called me, concerned that the he'd get sudden spurts of high pressure at times and that the Temp/Pressure valve (TPV) on the WH was leaking. He said it usually happened after doing laundry or taking showers. I asked him to get one of those inexpensive pressure gauges and put it on an outside hose bib. Sure enough, the pressure was spiking to over 100psi. The TPV was on the WH was doing it's job. This was caused by cold water entering the WH, getting heated (which makes it expand), with now (given the new check valves), no place to go so the pressure went up. Adding an expansion tank fixed the problem.
If this is your problem, the high pressure probably overwhelmed the shower valve. For further diagnosis, does the "spurt" happen from any faucet? Does it continue to leak after the short spurt? Like I told my son, you should consider getting a simple pressure gauge which are usually available in the plumbing/sprinkler system area of a big box store. attach it to a hose bib and see what kind of pressures you're dealing with.
That's just one possibility that I personally experienced. Crip might also be right in that if you have a pressure reducing valve it might be failing , but I would not expect that to be intermittent.