Have you seen this?
http://school.cucas.edu.cn/#Chengdu
I don’t have any personal experience dealing with this organization, but I’ve had a good look around the site and they seem to be promoting themselves as a portal for international students wanting to apply to Chinese universities from abroad. Seems like they help with all stages of the application process, including getting visas, etc. So if you do want to apply before you come, this might be the answer. I think it’s a government agency rather than a private sector firm, but don’t quote me on that.
I initially thought I could use this site as a springboard to find out about the programs and then get more information from the schools directly, but as far as I can tell now, the information on this website is about as high-quality as it gets. Like you, I’ve also had close to zero luck getting anything useful out the schools themselves when I’ve tried to contact them, either by phone or email. Even finding the right person/department to talk to takes at least 4 or 5 phone calls.
By the way, the only (very slow) email response I got was from Chengdu University, which, among other things, told me that all first year students have to live on campus(!?!) Still waiting to hear back if that includes non-degree Chinese language students or not…