Boerdoc, three showers @2.5 gpm = 7.5 gpm, plus a toilet or sink running, and you have no problem; and usually most showers are usually run for 10-15 minutes.
But run a hydrant at 6 gpm for 30 minutes and you're out of water because of the Pumptec if it is working correctly OR the low pressure safety cut off switch but the real cause is not enough water in the well OR the pump you have can not pump from the depth the well is being drawn to. Which is my guess.
I don't know pumptecs but I wonder why a safety switch with one.
I would not set the air pressure lower in my pressure tank because I don't think that an extra 1-3 gallons if that much, is going to matter because your pump will be putting out 2-3 gallons in under a minute and you're out of water anyway. But Valveman knows more about that than I do because he does it and I have never done it. I do know that with your large tank, or two tanks, when the pump is off your pressure won't be as good with less air as it would be with the right pressure in the tank and, you'll draw down the tank(s) slower which kind un does the constant pressure and other benefits of the CSV.
So I'd check out the pumptec to see if something is wrong with it and the static water level in the well and depending on the pump's age, look into maybe something wrong with it or I suspect it's undersized.
If the pumptec worked right you wouldn't need the safety switch and getting rid of it would stop you from going to reset it.
What was the need for the liner? Maybe the pump is getting hot and the thermal overload is opening, shutting off the pump while you're using water at the hydrant and the switch opens. That's a good probability with a 4" pump in a 4" liner.