I hate to say this, but it's in your head. That's not saying your concerns aren't valid, but just realize that it's a mental block you're having. The first time you go to a pole that's made from a different material is a scary thing, especially if it's a brand new pole that hasn't been "broken in" before. There's also a trust issue. Personally, I didn't find there to be much of a difference between brass and TG, but I also play on chrome at home.
If it's the studio I'm thinking of, you're also going from a 38mm brass to either a 45mm or a 50mm TG. The size change itself makes a big difference. Can you invert on the 50mm poles at the studio?
What I tell my students who freeze when they invert is that even though they might slide down initially, they will very rarely fall. To actually fall, you have to completely let go of the pole with your hands and legs. I've "fallen" out of moves (no limbs on pole) and still managed to catch onto the pole after falling a foot. Your body will instinctively reach out for something.
Anyways, just keep practicing on your pole and learn to trust it. When I first installed my XPert, I didn't trust it enough to go upside down because I thought it would fall on me. After a week, I had enough faith in the pole to try things. After two weeks, it was as though I was playing at the studio. I also got my boyfriend to just "hold" the pole whenever I inverted just to make sure it was stable for my own peace of mind. Can you get someone to "spot" you? Once you've done it enough and know that it's safe, you'll start to trust and be more adventurous. Sometimes, you just have to go balls out and go for it. If you're feeling like you don't have enough grip, get a grip aid.
Hope that helps! (The TG is so awesome--so jealous!)