Thanks to everyone for all the input. Great conversation.
And now, $0.02 from someone who hasn't touched any of this stuff. 
Hey, been thinking about this a little, here's a couple of other ideas...
1/ give contributors a way to tag their PRs so they can indicate how
important they think the PR is to b/ ansible project as a whole, b/ their
particular use case. I think it might help a little with the 'triage' side
of dealing with PRs, that is, working out when they should be dealt with. I
just had a quick look and the largest group of PRs I could find were P3
feature pull requests.
I believe not everyone will say every PR is vital to ansible and their
personal needs. In fact, My https://github.com/ansible/ansible/pull/9475 is
super low priority, so there's one less that needs dealing with any time
soon 
That said, from memory, github doesn't seem to have a facility for PR
submitters to tag their PRs like this, so it would have to be something
custom (which would take time) or a convention (which isn't then enforced),
so its not obvious how this could be done usefully.
Triage is so tricky to do well. I think we're better served generally
just to figure out how to get people to a place where they can commit
directly -- which brings us to the next point.
2/ slowly, and with advance warning, start raising the requirements for a
PR.
I'm just talking about requiring say, documentation or tests here, not
requiring particular coding standards. Obviously its in everybody's
interests that whatever becomes a core part of ansible is as good as it can
be. The more features that go into Ansible the more important it becomes
that the new features don't break existing ones.
So there's an important difference between "raising the requirements
of a PR" and "raising the requirements of a PR that is likely to get
accepted." It's very difficult to do the first, but pretty much
essential to do the second.
I think this is one of the key reasons why the focus on testability in
2.0 is so important. If we don't have a strong test framework, it's
easy for potential contributors to say "there's a hundred ways I could
test this, I don't know which one to pick, I'll just leave it."
Whereas if there's a standard for testability, and part of the PR is
"here's evidence that my PR isn't a breaking change," then it becomes
more defensible to just merge changes.
Of course, that's still in the future. But it's a closer future now, I hope.
But.. maybe this would just be against the spirit of Ansible? Contribution
seems to have been 'on the front' page of this project from the start.
Plus, it might not always be viable or even valuable to insist on tests.
(I'm thinking of things like the filters which are often very thin wrappers
around python functions). Should they be unit or integration tests, or
both? Some thought would need to go into changing the contribution
guidelines so that they don't result in confusion.
Ayup. Lots of work here.
But this is also one of those places where we might see some payoff in
the module split between ansible-core and ansible-extras. The point of
that is to be able to lower the barrier, and to give us a "contrib"
space to prove out some modules that we don't necessarily want to ship
to all Ansible users... yet. That obviously doesn't help us with the
current batch of core modules -- but it could be argued (and has been)
that we have too many core modules anyway. Maybe a rigorous
examination of which modules are truly "core" is in order, and modules
that don't make the cut can be kicked into extras (and thus
potentially to the maintainers who are most interested in them.)
Another idea that I had, which I don't really think would work but am going
to share anyway is to give someone access to commit documentation only
changes. Maybe this would take a bit of work off the core maintainers, but
looking at the current PRs there aren't that many that are tagged as
documentation and I think there's probably a surprising amount of work in
there to keep things in sync with what's actually in latest devel branch.
Hmmmmm. Interesting. Doubly interesting because there's also an
i18n/l10n issue here, and splitting out docs also makes it possible to
split out translation of docs. Need to figure out how to make that
happen.
Well anyway, hope something from the above is of use.
Got me thinking, anyway. 
--g