A automotive switch isn't going to be able to handle the current required to start a motor like your wanting to do. That said the best way to do what your needing is to use two motor starters. The best way to explain it is this is that it's wired as a push to start/push to stop circuit. In other one starter is wired with an auxiliary contact so it pulls in and stays in when the start button is pushed. The other contact is wired to where it only pulls in when the start button is pushed. You should be able to do a search online to see how it's wored.
Doing it this way gives you a momentary switch (as long as the start button is pushed) that pulls in and engages the capacitor start, and the second starter that pulls in and holds to keep the motor running.
I wired a 10HP 3 Phase motor this way to use as a rotary phase converter and it works great. In my case the 3 phase motor needs the capacitors tied in on the third leg to get it started spinning, similar to the way a single phase, capacitor start motor needs the capacitor to get it spinning. Once spinning the capacitors are dropped out of the circuit, in most cases by a centrifugal switch, but in this case simply by releasing the start button and letting the starter wired for momentary operation open and drop it out.
Like I said I did mine awhile back and it works great so I don't see why it wouldn't work in your application also. The only drawback is the starters aren't usually cheap if you have to buy them new. I got lucky and got a few from the place my Dad works that came off pump controllers that they had removed from service. That said if you don't have the starters on hand try calling around to some places that do municiple type well and sewer equipment repair. If they are like where Dad is they pull at least one controller or two a week that has a good contactor in it but another bad part that keeps the whole thing from working properly.