How can I reclassify in the National Guard?

Call the unit you want to transfer to and talk to the AGRs there. They can tell you what slots they currently have available and if they are willing to send you to school to reclass. If they have a slot for you, get the para/line number. Then, go talk to your full time unit staff (FTUS) at your current unit and send a request up to your commander to transfer. If your commander approves, your FTUS can initiate the dmail 45 with the para/line to start your transfer process. Ultimately, it all hinges on your commander releasing you, but I find it helps if you do the legwork yourself.

On the national guard side you need to talk to your readiness NCO along with a recruiter to see if any of those slots are open and to see what requirements need to be met for the school

Technically as long as you filled your original obligation with your contract, and your ASVAB scores meet requirements, you can reclass. I would look for retention in your area (similar to recruiters, but their sole job is to help those already in, stay in with the jobs they want). Retention can make inquires into those units to determine open slots, and make contact with the commanders to see if they will take you in. Usually it's easier to reclass when already xferred to the unit, but not always. Retention should definitely help.

OJT is not a thing. Talk to the AGRs at the unit you want to transfer to.
Get them in touch with your unit, have your unit start the transfer.
You can transfer and to a pretty short reclass to 11B or 88M. Most reclass schools at RTIs are 4 weeks.

I have tried twice to reclass in the Guard, both times I was denied. They typically will only allow you to reclass when you are re-uping ... but maybe and hopefully you will have better luck!

Talk to the recruiter from those units they will be able to answer your questions. And yes it is possible, and depending on your ASVAB scores would determine if they could waiver you for OJT or if you would need MOS school qualification.