I've recently been losing water pressure as the pressure tank drains to the pump cut-in. the switch trips, but there is a delay of 2-3 secs before the pump is able to recharge the tank.

I've checked the tank pressure a few times. It always reads ~28# or whatever I've pumped it up too. The tank is the same as when we moved in, so its at least ~5 yrs old. I'm pretty sure that is got a slow leak to the point that I need to add a few #s every 2-3 months. There isn't any water coming out of the valve, so I don't think that the bladder is blown. I've also noticed that the pressure gauge mounted on the line reads ~10# less than what I read at the schrader valve with a typical tire gauge.

What's odd is that the pressure switch trips ~30#, but then the pressure on the in-line gauge instantly drops to 20# or less (sometimes nearly to zero). Its only 2-3 secs before the pipes jiggle a little & the pressure quickly shoots up. I'm not sure if the is a delay in the pump spinning up or if there is a delay in the power getting to the pump, or sticky check vavle, or..

My vote goes to the sticky check valve. A instant pressure drop means one of two things. A break in the service line or a check valve that's losing pressure back down the well. Regards, Tom

Is it worth the trouble of pulling the pump (its about 260' down a 360' well) for a sticky check valve or wait for it to fail completely? Any reason not to install another check valve between the tank & well?

" any reason not to install another check valve between the tank & well?"
Non what so ever. But I would install it between the pump and the well. This would retain prime in the pump. Rather then pull the pump that's what I'd do. It's the cheapest way I know to see if the old check valve's faulty. Good luck, Tom