Clean up the construction-time arrangements.

There was all sorts of code here that pointlessly pushed the bulk of
the constructor operation off to instance methods, which (a) could
cause confusion when there's bona fide trouble -- that is, it's better
to throw in the constructor -- and (b) didn't really help with
efficiency in any realistic scenario -- that is, while the original
code nominally avoided extra work until first use, in practice first
use occurs immediately after construction (and in the same thread,
even).

Now, all the one-time work happens in the constructor, and we get to
avoid asking "am I set up yet?" before doing anything substantive.

While I was in the territory, I also did a bit of more minor code
hygiene maintenance.

Change-Id: I41225d373e3ab481b6bc3da5b74bde89c4fd895e