Thanks to all for your helpful suggestions. After discussing various
options with DH, here's what we're going to do for at least 10 days.
Pantley claims 10 days, if at that point it's not working, we'll
reevaluate and if it looks like we're making progress, we'll try
another 10 days. If not at all, then we'll re-think it.

*keep DD in our room where she is now
*take the arms off the crib (it converts to a toddler bed)
*move the crib right next to our bed
*when she wakes, not pick her up, not nurse her, but try to soothe her
back to sleep with pats on the back. This may require me to have an
arm on her for awhile.
*if she gets to screaming stage I might sit with her or walk to calm
her down, though I'm not sure if this will throw things out of whack
or not
*make sure as much as is possible that she's well fed before dinner
(although we always try this, some nights she just won't eat)
*keep a consistent bedtime of 7:30
*keep the bath at night for now, since overall that works best - it's
not every night, more like every 3rd, but if it appears that the bath
is winding her up, we'll change that
*offer her only water if she does wake up
*On nursing to sleep, I think I will still nurse her, but do it
sitting up and then lay her down awake rather than nursing laying down
to sleep on the bed as we do now. She fights this already, but I'll be
tough.

I'm holding off on the white noise for now as DH is unwilling to move
beds at the moment and that's not yet a battle I feel I need to fight.
If we're making no progress with all of the above, I may insist upon
it for at least a few nights and try a fan in the room (and he can
either move rooms or tolerate the fan. He is getting to desperation
stage but he's not quite there yet).

If after a month or so we're nowhere near close to sleeping longer
stretches, I'll see if it seems our presence is the problem, and then
we'll move to another room and I'll fight the battle with DH on the
bed. I won't be buying a new mattress. We won't be buying a new house
with lots of rooms ;-) I'm also not inclined to do a lot of work on
another room as a temporary solution since every weekend doing that is
a weekend away from working on DD's room, which is the priority (we
have too much experience of starting our priority project, only to
have another project come up requiring our immediate attention and
then everything else gets pushed back another month).

I've decided we'll tolerate the night wakings or resort to CIO at that
point if we have to.

Thanks again for all your suggestions. I really appreciate the help.
I've decided for my next child, I'm ordering a sleeper, with a really
calm personality ;-)