I thought you (and perhaps others) might find this interesting.
In preparation for going through your Manual again, I started reading my notes from Sailhamer's Advanced Grammar class in 1986. I knew I would find some similarities in your approaches, but I'm amazed to find so many in the first half hour of reading. Sailhamer was ultimately interested in the levels above the clause, which he called Syntext. Anyways, he spent a lot of time explaining clauses so he could get to combining them into sentences (two clauses, following Anderson), and into larger text segments. I have to say that so far it almost sounds like reading your Manual and a few things you wrote to me privately. His analysis pretty much follows your syntax diagrams. He even said every phrase needs a head, it is obligatory, and talked about nulls. So I guess it was my bad to not remember that. So far in my reading he didn't use the terms compliment/adjunct, but obligatory/non-obligatory constituents.
But, I was shocked to read this, because I didn't ever remember him mentioning this. Although he was mostly speaking of how clauses related to one another, he said this in July 16, 1986, (from my notes, there are probably lots of nulls)
"- valency - capacity of certain configurations of elements to bind themselves together in chemistry
- can put words together, high valency
- operates at level of individual words to whole texts
- i.e., not as two south poles on a magnet, holding them together, we want to turn magnets around, n and s poles, let the magnets go, and they stick"
If I find anything re his theoretical leanings, I might pass them along also. I think I know, but I have to be sure.