From the run times you stated, the biggest problem you have is well production. It should fill that tank between 30 and 50 lbs in less than a minute if the well produces good.
I was wondering the same thing. My experience with a shallow well with this type of pump was poor, we had a 45' deep drilled well, about 20' from the house. during the 8 years i lived in that house, we learned to manage with low reserve, quick showers, and managed when laundry was done vs dishes vs whatever.
at the time i sold the home last year, i knew it was going to be an issue. my thought was to try a submersible pump (110v) with the idea that the submersible would
pump from the bottom of the well and we hoped recovery was better at the bottom. everything i read and was told was that the inside jet pump could only pull water from 25' deep (or 26). once the water in
the well dropped to a certain point, the pump would continue to run because it didn't have the strength to "PULL" the water up with enough volume to satisfy
the cutoff switch. if it would continue to run too long, i had to run down and kill the breaker and let the well recover a bit then start it back up. we would never run
out or suck air due to the water always being above the pickup, but after a long time running the pump you could tell the pump wasn't happy.
as the sale of the house progressed, and the submersible pump didn't improve volume, i had to install an inside storage tank system with UV to satisfy the
bank requirements.
in this case with the OP what is the height difference from your pump to the static water level? and then how low does the water level drop as you are running your garden hose?