How can I drop my promotable status?

There are a few ways that you can stop being promotable, simply by letting your APFT or weapons Qual expire. If you are promotable by MLI then you can't become non promotable unless you're flagged. I have seen someone voluntarily waive their promotable status by a memo, but that was before MLI.
Secondary consideration is that you might waive your status and then be denied for your MOS request. Blackhawk mechanic is not heavily under strength and HRC may decide that the strengths don't support your request.

CPL (Join to see) If you have already been boarded, you will not be able to drop the promotable status; however, you can decline the promotion (but that's usually not looked at favorably). You'll also have to look at the IN/OUT calls for each MOS you are looking to change. Talk to your Career NCO for more information.

SFC (Join to see), any advice?

Fill out DA Form 4187 Request for Personnel Action, bearing in mind that if your pmos is under strength then you porbably won't be allowed to reclas anyway.