I can't speak for Zen, only a little about Taoism.
I'm surprised to read "a Taoist himself" describe Taoism as "seeking attachment".
Instead I think that Taoism seeks some non-duality; and especially a harmony or a proper balance (e.g. between Yin and Yang ... not exactly a "middle way" necessarily -- i.e. sometimes what's appropriate is a lot of yin with just a little yang, or vice versa).
I think that (IMO from a Buddhist or a "personal" perspective) perhaps there is some attachment e.g. to the body -- but it isn't described as such, instead there's a quest for longevity (or immortality), or youth (pliant like a young reed rather than breakable like an old stick), is maybe one of the goals or ideals of Taoism -- with death and disease being described as an imbalance within the body (or between the body and the world) -- this is the subject of Traditional Chinese Medicine.
I'm not aware of (not privy to) the more mental or doctrinal aspects of Taoist training (partly a language barrier, i.e. me not understanding the Chinese language). A practical or physical aspect of it that I met was some kind of autonomicity -- for example, when practicing the art of hand-writing it's maybe better not to stop and think about that too much ... instead just kind of do it, carefully but automatically, maybe relying on training, maybe "reacting appropriately" without thinking about it too much or getting lost in details.
So see also for example:
Acting on your non-conceptual (pre-conceptual) knowledge/wisdom/intuition is one of the most important Zen practices
I think that kind of getting out of the way and doing things naturally is Taoist.
Though I think there's also (apart from, you know, not thinking) a lot of scientific or pseudo-scientific knowledge, about medicine and so on.
I think a corollary, too, of doing things naturally, is maybe not stressing about stuff under pressure.
There is such a thing/practice as Taoist meditation too ... so maybe it has that is common with Zen too (i.e. the existence of sitting meditation as a practice). I think the form of Taoist meditation I was taught (i.e. visualising something in the body) is unlike the form of Zen meditation but, who knows, maybe there are several different forms (and I was being taught a very elementary or beginner's form).
Also perhaps you're ignoring the possibility of evolution. When I read that, "Chan = Buddhism + Taoism", I thought that was in the context of describing a historical/evolutionary event -- which happened over the course of centuries and more than 1000 years ago, in China.
So I wonder if maybe it's like, saying, "English = Germanic + Norman", and asking, "How do English-speakers combine Norse with Latin?" It's a legitimate question but not a practical one.