TSS for mountain athletes is fudgy at best anyway, so as long as you’re consistent in how you use it, I think tTSS will work fine. Here’s a TP article on estimating TSS: https://www.trainingpeaks.com/blog/estimating-training-stress-score-tss/
Another option is to tighten the chest strap (which you’ve probably already tried) or to get a new strap that’s “stickier”. My straps are all pretty old, but out of them, the Wahoo strap is grippier. There are probably other options as well.