Let’s look at your questions one at a time:
Is there a new SOP for battlefield promotions?
SOPs are produced locally (at the unit level) to supplement regulatory guidance and unit procedures not covered by regulatory guidance. Based on the information below it does appear there may be a local SOP at some level for Battlefield Promotions.
Also what exactly are the requirements for it?
Please see the information below
Do Special Operations Support Elements have a different process for these things?
I cannot address this specifically but I would imagine they would have to follow the SOP and regulation in place at the specific time in question