I am not aware of any 1/4 HP submersible pumps for going down a well.
In selecting a pump for an application, the depth to the water is what is important, but not just the depth when water is being drawn, but also the depth that it pumps down to during use. It is still good to know the "static level" -- the depth the water is when it rests-- when selecting a pump.
Calling a pump by its horsepower is only part of the story. The gpm rating is important too. A 1/2 hp 10 gpm pump cannot develop as much pressure for normal household use as a 7 gpm 1/2 hp pump can. A 10 gpm pump is usually cheaper than a 7 gpm pump because it has fewer stages.
Did this pump give good performance for you when it was new, and then got worse? Or was it like this pretty much from the beginning.
Pump runs several minutes like 3-4 minutes before it shuts off.
I was not expecting you to say that. Your problems will not be helped by a new pressure tank. Three to 4 minutes for a 20 gallon tank is unheard of unless you do have a CSV. But if you had a CSV, the pressure would build much more slowly in the second half or so of the pressure rise.
That's a good sign. We would not want the pump running out of oomph as it approaches the cut-off pressure.