I'll soon be launching a reference site called Thunkpedia which loosens the 'encyclopedic' standard, but adds other constraints in its place.
There's a video about my motivations, and a sneak peek of its interface, at http://thunkpedia.org. More discussion is at the project blog, http://infinithree.org (from the original codename).
Wikipedia is still very good, and a fork with the same 'encyclopedic' mission, software, and general format – but inclusionist – would inherit all the stresses that made Wikipedia become deletionist. It'd also still have to compete with Wikipedia for the critical mass of attention and contributors who like everything about Wikipedia except for the deletionism.
The reference-information successes have explored territory a bit further from Wikipedia, in content (Wikia, wikiHow, tvTropes) and format (StackOverflow, Quora, IMDB)... so that's what Thunkpedia is doing too. Whether it succeeds or fails, it won't fit neatly into your list of 'inclusionist Wikipedia forks'.
> Wikipedia is a free encyclopedia, written collaboratively by the people who use it.
There's the problem. Wikipedia should stop being an encyclopedia and start being Wikipedia.