So based on my experience with the PA school application process, there is a high probability of not making it in the first round. Nothing personally, but there are waaaay more applicants than spots available, so competition is high, and your competing against premed students who didn't get into med school and now want to take their 4.0 full time student college GPAs and try the PA school route. So don't be shocked if you don't get in the first time.
That being said, if you just need 150 more patient care hours, getting hired by a county system only to get 150 hours sounds like a lot of time and effort, when there are better things you could be doing. I mean, if you will be doing 12 hour shifts (which is standard in EMS), you'd have that done in 13 shifts, which can be completed in less than a month. If you I looking to do EMS as a career, or as a career until you get into PA school, I would definitely look at other systems. And if you do get accepted, you won't be able to work while you are in school, so make sure you have a way to support yourself for the next two to three years of your life