Unless your pump also has a control box, one of my wells does, there are only three possible problems as you know.
A bad breaker will buzz sometimes and trip IME. Sometimes they just trip instantly which IME usually means a short somewhere. But Breakers work off of a heat sensitive spring which can be “taxed” after being subjected to high power demand. ‘Heating’ it up on a regular bases but just below the point of tripping which shortens its life span.
The pump maybe on its last legs, maybe a bad bearing which is causing a ‘drag’ when starting up which would cause a power demand ‘spike’ above what the breaker can handle. Kind of the same when using my small table saw and ripping large thick material and the blade gets ‘pinched’ and the motor struggles and the breaker trips. Especially if connected to a extension cord.
I have had pressure switches go bad. But they did not effect the Breaker. Pretty easy to swap out as I am sure you know. See no reason why you can’t use a properly sized crimp connector. Buy a couple of commercial grade. There are pressure switches to be had that have clamp connectors. Just strip back the wire end to the proper length and stick it in and screws tight.
I would start with the cheap and easy stuff. Buy a new breaker and pressure switch. Install the new breaker first and see what happens. If it trips install the pressure switch. If this doesn’t fix it then it kind of has to be the pump.
You can leave the new stuff in place or take it out reinstall the old and return the breaker and pressure switch for a refund.
I have only worked/installed a few well pumps. Not familiar with the many different types/brands. The ones I use have an internal thermal switch/breaker. To protect the supply line from being overloaded when it fails. The ‘switch’ is not replaceable.
Replacing the pump itself is pretty easy. Well electrical line water proof spice kits can be bought for a few dollars.
Pulling the pump is where the real work and hassle comes into play. Especially with 1200 feet of pipe and wire to pull out. It will require a couple of people to help. One to pull it up and another person or 2 to walk/lay the line out.
Or rent one of these. I have never used one.
http://www.gappower.com/Rent-an-UPZDAZY-Well-Pump-Puller/item/PUMPUL
You also need to MacGyver up a T-handle that screws into the pitless adapter. Made one from black pipe threaded on one end. The size is based on the size of the adapter
https://www.google.com/search?q=pitless+adapter&rlz=1C1AVNE_enUS611US612&espv=2&biw=1600&bih=775&tbm=isch&imgil=2JZsKak43AzAiM%3A%3ByFv1RAT-ytXyNM%3Bhttp%253A%252F%252Fwww.deanbennett.com%252Fpitless-adapters.htm&source=iu&pf=m&fir=2JZsKak43AzAiM%3A%2CyFv1RAT-ytXyNM%2C_&usg=__5lw7VCDBHRWietPwCxNEyO89n6s%3D&ved=0ahUKEwiD2-elzvLKAhWCTCYKHeXYBOAQyjcITQ&ei=wAO-VoP7BYKZmQHlsZOADg#imgrc=2JZsKak43AzAiM%3A
to disconnect the supply line from the stand pipe.
Or as you said call a well guy. Not going to be cheap. We lost a pump and control box to a lighten strike on one of wells. Our Home Owners insurance covered the cost less the deductible.
You may know all of the above. As usual with my posts/comments I included more information for others benefit who may not.
Let us know what fixes it. Good luck