I'm reluctant to say too much on this because IME people like things to sound mystical and arguing with that is pointless. But here goes.
One, you have a lineage any time you study with a teacher. But there is no "one" lineage for changchuan. As I already informed you, the term "changchuan" refers to several different martial arts under one umbrella term. So there is no "full lineage transcript" as you mention.
Second, the term shaolin gets thrown around a lot. That doesn't mean the art in question came directly from the temple. I've looked at your curriculum page and most of what's listed are common forms here in Taiwan. (I've lived and trained here for 8 years.) Nothing whatsoever wrong with that! They're good forms, likely better than what you'd get elsewhere. But they aren't official "shaolin" forms. They're possibly shaolin derived, but that's it.
Third, Chen Sui-cai was mainly known for hongquan, if I remember correctly. The more commonly seen name for that style is "hung gar" although the characteristics of the hong quan in Taiwan is slightly different from the more common Hong Kong version. I trained this style for a while and it's good stuff. Stick with it.
Fourth, the long fist that you possibly got through Fan Chi-sau was from the Nanjing Guoshu Academy, meaning that it's a mixed group of stuff they put together. Many elements of various long fist systems went into it, so there's no real lineage associated with it, per se. The lineages that have been derived from it tend to be grouped around the teachers that learned there and taught it -- like Han Qin-tan, a famous long fist teacher that came to Taiwan.
Anyway, enjoy the training.