Anyone have any tips for getting a recommendation from a chain of command that doesn't know me?

You have to wait one year to meet time on station requirements before submitting any reclass action so that will give you plenty of time to get to know them.

You will probably need to give it some time to process as you are new to the unit. Act like an absolute stud for your CoC to gain confidence in you. Think long and hard on why you want to switch MOS's so discussing it sounds natural. Ask for an "interview" with the 1SG or CO to gain their support in this endeavor, and to help coordinate another "interview" with the LTC or CSM for their favorable support.

It will probably take some time. You need to be good and what you do. Be Johnny on the spot. Good PT, uniforms and the like. Use your chain of command and talk to them about what you want to do and why you want to do it.