Does anyone have any experience in getting a school training slot from another unit?

I admire your pluck, but that's not how seats work. Even if you could request it from another unit, you have a UIC and ATRRS doesn't work that way.

Theres a couple of ways to skin this cat. First is to get yourself to a culture where this is normal. USASOC, RTB, even aviation, get slots at SERE. Some units just have more cool guy schools than others. The other way is to walk on to the school. That only works for a handful of schools. People are not lining up to walk onto SERE. Almost certainly there will be unfilled class seats. Every school in ATRRS has a minimum requirement to run a class, an optimal number, and a max. Some schools cannot run a class unless walk-ins show up and meet the minimum number. Contact the school you want to attend and ask. SERE requires a SERE physical, NDA, and clearance to attend.

Asses to join the 160th. As a 92A I got schools like Airborne and SERE C from being in the regiment. It’s great for your career and will open many doors for schools.

Just put in for it. You'll be on the wait list to see if there's any openings for the course you are trying to get to. The unit having a slot just means they can guarantee you a spot in a specific class.