how to add air back to a water pressure tank

We have an older well system in a house that we purchased this summer. The information that I have found on the web assumes that there are some valves in the system that I don't have, for instance allowing me to drain the tank or bypass the water softener.

Well and Pipes diagram

There are a couple of other valves I left out, but they are not helpful, they just allow you to shut things off before or after a component so I left them off the diagram.

The pressure switch is set at 40/80 psi and the pressure tank is probably 75% full of water based on the line of condensation on the outside of the tank.

The directions I have found talk about draining the system, then pressurizing it to 25psi, then turning on the pump and flushing the system at a point before the water softener. I cannot do that since I don't have any points to drain from and I cannot get any water out to the system before it hits the house or an outside irrigation hose bib.

My plan is to turn off the pump, attach air compressor and open a faucet, so that I can basically replace water in the tank with air and stop when the tank is 30% full at 40psi. Then I would turn the pump back on and hopefully be good to go.

This is the way it feel like the system is intended to work, is that the case? Or is there a better technique that I should be using?

Edit #1: In response to the comments I don't think that I have an X-Y problem here, clearly I have a waterlogged pressure tank and I am trying to fix that in order to reduce the rate my well pump is cycling at. I know the what, I am uncertain of the how in the case of my older system.

@jsotola I don't want to sound pedantic, but I'll explain it for anyone else who might have similar questions. The purpose of the pressure tank is to smooth out the operation of the well pump, so pump will compress the air in the tank up to 80 psi and then when you open the tap the air pressure is what actually pushed the water out or the pipe. Then when the pressure drops to 40psi the pump will turn back on to repressurize the tank back up to 80 psi. If we have 1 gallon of air at 40 psi, then at 80 psi that same air will only take up .57 gallons, so in the case of my 40 gallon tank having 25% air at 40psi means that the tank will only store 5-6 gallons of water. If I start at 70% air then the tank would store 16 gallons of water and the pump would cycle significantly less.

The reason I was suggesting 70% was that I did not know if the pressure switch had to stay submerged.

Edit #2: Here is a picture of the tank in question. It is one of the old ones with no membrane.

Pressure Tank and Well

Edit #3: I'll start with the embarrassing news, when I got into this process I realized that there was a hose bib mounted right next to the ball valve. It was covered in black goo and blended in with the permanganate container, but this made flushing the tank more practical.

Before that I had been filling the tank via the Schrader valve and it was making progress. But then I noticed the valve I had missed before. So I, just drained the whole tank at that point.

I pressurized it to 37psi then turned the pump back on, everything filled up nicely. I then opened up the valve and flushed the system for a while.

This is a graph of the pump activity before and after the process: pump activity over 24 hours

The pump is cycling much more infrequently. I guesstimate that I am losing about 20 gallons of water an hour, so that is my next issue to resolve.