There are many who post the life expectation on a pump is maybe 8 or 10 years. I think that varies with conditions. In 2014 I got my pit demolished, the casing extended, and a pitless installed. I opted to have the pump that had been installed in 2002 put back rather than replacing. But it was working nicely. You have the symptoms of a failed pump.
To work around this, for a few days, can you crank the pressure switch range nut clockwise to increase the cut-in pressure and
counter-clockwise to lower the cut-in pressure (on the big spring) enough to get the pump to shut off? I don't know if you can go that low. Then the precharge should be adjusted down to 2 PSI below the new cut-on . Normally three and a half revolutions of the range nut will change both the cut-in and cut-out settings by approximately 10 psi. Just consider this temporary. Get the pump replaced. The pump will progress in the bad direction.
Get the pump replaced. Think of the $30 or so water bill that you have not had to pay during those 10 years. This is important enough to allocate money away from cable TV or restaurants. What does your fiance think? When you do get the pump replaced, while staying out of the way of the workers, collect data (clear photos of model and date code labels on pump on the top and the motor on the bottom) on the old pump, new pump, how far down the pump is set, how far down the water is (static level). To know the static level, look at the waterline mark on the pipe.
For your filtering, how long does your sediment take to settle? Maybe wash one of your used cartridges in a bucket. If there is sand in the bottom of the bucket, then you have a fair amount of heavier sediment. If it is heavier stuff where a fair amount settles soon, consider adding a Twist2Clean filter in front of the cartridge filter. If your sediment does not have much that will settle out, consider a bigger sediment filter or a backwashing filter. A backwashing iron+sulfur filter will double as sediment filter. It would normally be the first thing after the pressure tank. What does you fiance think of the taste/smell of your water or the color of your toilet tanks?