I'm a former kung fu practitioner but I can't tell you. Chinese lineage is extremely obfuscated and obscure in a lot of cases. That and there are so many different arts it is very difficult to decipher. I have confidence in my personal training, but that is because I did roughly 2 months of research into the art and the teachers, lineages, and locations before I even started training.
I sympathize with you, I've been there before. Chin na is essentially joint lock study, so is not a "style" per se. It is incorporated into many many different chinese styles including tai chi (which I also enjoy) and every style has their own uses and takes on it. Tian Shan Pai I know nothing about.
I am personally biased towards wing chun, since that is what I did, but you do need to look into the school and the methods of practice (do they do free sparring, etc). It is also hand heavy so if you like kicks it is not an art for you.
Although I will say if you are practiced at free sparring already, and contact, then wing chun is conceptually simple and can be learned through that prism and applied as you see fit in whatever style you prefer (Joe Frazier learned a fair amount from Bruce and has been documented as saying it was very useful).
In general I say start and see if it passes your smell test--that's really the only way you can ultimately know even if you have a lot of research into a style. But I definitely suggest doing as much "due diligence" as humanly possible with TMA's and especially with chinese systems since there are a million of them.