HH, I know what the Dramatists Guild is; I've been a member for over 30 years.
You are correct that the Guild is not a union and doesn't enforce a "minimum" in the way AEA does. But throughout my membership it has set "recommended minimums" for different levels of theater (as well as other recommendations in sample contracts). The custom (and the last time I checked, the Guild recommendation) was 6% for the various authors of a Broadway musical. As I mentioned, such authors are often asked to take cuts, so "minimum" to an author is different in several ways from "minimum" to an actor.
Adam's question regarding rights to source material is a good one and I don't know the answer. My guess is it depends on the clout of the writers of the MUSICAL as to whether source rights are paid out of the show writers' royalties or not. (Obviously they didn't pay Doctorow 9% of gross out of Ahrens/Flaherty/McNally's 6% (not even if the 6% were a little higher due to McNally's track record)).
I don't know how option agreements are generally worded at The Public, much less what specific arrangements were negotiated by Miranda. But the only NY option I ever signed covered Broadway rights and the producer's participation in post-Broadway subsidiary rights; it said nothing about an off-Broadway production. That was obviously the opposite of HAMILTON's situation, but merely saying "That's what option agreements do" hardly answers anybody's question.
The name producers of HAMILTON (i.e., those other than The Public) were all producers of IN THE HEIGHTS. It is not impossible that Miranda shares the participation of one or more of them. (As I wrote above, Michael Bennett did for A CHORUS LINE.)
Since Miranda already had a Broadway hit under his belt, I don't think 10% for writing book/music/lyrics and arrangements and starring in a show is beyond the realm of possibility. If you are "extremely sure" otherwise, HH, I'm willing to concede the point, but I'd like to know how you know. (In general, I mean; I'm not demanding personal information from you.)