TLI is really flexible in these matters. I just did a 2-week course with them last month in Kaohsiung, but I've done similar things at the Taipei centers over the years as well. The director in Kaohsiung told me that TLI is taking personalization and flexibility for working people as its direction to differentiate itself from the other language centers.
TLI's OK. The organization is a bit creepy. Lots of old WSR battleaxes running around. But by Taiwan standards for language teaching, they're not bad. I'd hate to work for them though. That may be the source of your Shi-Da teacher's bad feelings since there is quite a bit of overlap.
I know a couple of really great private teachers. PM if interested.