I heard a rumor they will be have the application open soon. The folks at KCC will usually send stuff out if your on there email listserv because you took stuff through KCC EMS. The application stays open for less than 5 days and you must have your state license and NREMT. It's now required as of like 2 years ago to have NREMT to keep your state license. If you have that then your good. The medics prep the EMT's to go to medic school within two years. After a year with City you can can apply and they will pay for you to go. Most get in around the second year. Some take up to full contract year of 5 years.
I have heard rumors they will have a application very soon and it's based on the needs and usually closely follows the KCC fall and spring schedules. I know they will have one next May supposedly one in the next couple weeks but they could hire folks in May of next year instead. It's usually open twice a year. The only way to know is to check ever day since once the application is full they close it. It could stay open less than a day in some cases in which you would have missed it. Just keep checking ever day.
If you do a program on the mainland. You do the transitions program and life a little bit more challenging but they need medics. You will just stick out a little more and even if you have your medic they may encourage you to redo it here which some people have done. Getting your state license is a process from out of state if you have not done it. I know they changed the process but it's mostly based on your education. They require 135 hours of ride time for EMT-B and way above NREMT for Paramedic. Make sure your program gave you enough hours. PHTLS is requried, Blood Borne Pathogens, you need an IV course, and manual cardiac defib course and one or two other things. Paramedic has extra stuff required beyond that. That is for State of Hawaii EMT-B. Then it takes about 1-3 months to get your license in the mail. If you need the extra ride time then Kapiolani Community College or KCC is the place to go. If you serious on that then go for it but it's not easy. I did it. It wasn't easy.
Getting a job may take awhile. One local hospital took 1.5 years to call me back on job. Luckily I already had one in a ER I didn't care. If they open up applications in January and you apply and pass the HR test you may start by like March to April. It's a process. I can say the previous threads and most of the things I wrote have not changed. Unlike on the mainland change is slow in Hawaii. Hope this helps.