I think you have two completely separate issues that you became aware of at the same time, and which are mostly unrelated.
Improperly set system and air pressures in bladder tanks.
A note - the higher the system pressure, the less water storage (drawdown) in a bladder tank. So you might get better performance from a 40/60 or 30/50 setting.
You are also at risk of damaging the bladders by underfilling the air for the pressure you have set on the water side. The bladder becomes much more distended than it's designed to be, and lots of water simply sits in the tank with the effective volume of the tank greatly reduced, since the first water to enter the tank is raising its air pressure from your too low setting to where the pressure switch is set, and shrinking the air bubble to do that.
Low pressure on the second floor bathrooms is probably from a blockage.
Pressure due to elevation is 2.3 feet per PSI, so pressure on the second floor due to elevation is probably not really the issue (might be 8-10 PSI less than the basement in a typical house) and of course it worked fine until you drained the system; so it's not "really" pressure loss, in the sense of the pressure in the pipes - IMPE it is often the case that when you drain and refill a water system "crud" (usually harmless, but unappealing, deposits from the water) in the pipes gets knocked loose with all the bubbles passing through and will plug shower heads and aerators - that does cause pressure loss OUT of the showers and sinks. Try removing shower heads and aerators, cleaning them, and blowing the pipes clear without having them in place.
I would suggest draining the system again, verifying that the air pressure is still 38 (if not you may have a leaky bladder) and resetting the pressure switch to 40/60 (with a typical pressure switch, be sure to turn the pump breaker off before adjusting.) Then remove all showerheads and aerators, repressurize the system, and blow the pipes clear before reinstalling the cleaned showerheads and aerators.
The check valve may be sticking open, and only closing when a considerable backflow (from the pressure tank the pump just filled, towards the well) sets up after the pump shuts off (when it "slams" shut as sufficient flow unsticks the check.) Replacing the check valve should solve that issue, if that's the issue. It might also have a broken spring, and possibly a new spring could be found, though I'd bet that might be harder than finding whole new valve.
One sticky check can do this all by itself.
IIRC you can get some non-intuitive problems from multiple checks, too.
Best Answer
The systems I've worked on have the filter between the tanks and the house supply line. You don't want to restrict the flow from the pump. what size is your house supply line?