Hello chaps.
PDog, I reckon it's worth giving the 2-3-4 pattern a go. One of my friends with a DS your DD's age (who's not a great sleeper) has had similar problems with him not wanting more than one nap. She's cut down to just one nap, but he does sleep for 2 hours then. It's young for going to just one afternoon nap, but some babies do at this stage. However, given how overtired your DD is, I think the 2-3-4 is worth a try first.
IC, I'm glad that having your DD in her own room worked well.
Curly, I think some babies do scream when they get overtired - they just can't go to sleep or stay asleep without doing so. It could be maybe general overtiredness even if that particular day's naps have been okay?? 
I think we may be officially in the 9 month sleep regression. We've had a lot more short naps than usual, especially at lunchtime but also in the morning.
The last 2 nights DS has been awake for 1.5 hours from around 21.30 (he's never done this before) as well as awake for another 1.5 hours from around 4.30am (normal when he gets overtired). He looks tired, has red eyes and was screaming at bedtime. :( It felt like a throwback to the bad old days of the challenging 3 month olds thread.
Recently when he was up, he was happy to roam around his cot in the dark while I dozed in bed till he got drowsy & needed patting/rocking. But now he gets really cross if I leave him in his cot so I have to spend my awake time rocking him.
On a more positive note, though, when I rock him for naps, I've been singing to him. When I'm rocking in the night, I'm humming the same tune, and he now usually puts his head against my chest even if he's not actually drowsy, rather trying to poke my eye out / bite my shoulder / pinch my throat. That's definitely progress! :)
Moxie describes this regression as 'you've got a brain working on developmental stuff that won't let the kid sleep, a brain and body working on movement that won't let the kid sleep, and maybe some random shooting or throbbing gum and jaw pain in there, too.'
I thought we might get away without the movement / teeth complicating things, but DS started pushing up onto all fours at the w/e, and pulled up from lying to sitting on his own for the first time today. One tooth is coming through and another will shortly follow. So I'm not surprised it's all hitting us now.
Tomorrow night I'm going out for the evening and leaving DS with DH for the first time since he was born - assuming I can get him off to sleep before I go. I hope they both survive!
I think I'll do both his naps on my lap tomorrow as he often wakes 5-10 mins after putting him down for the second sleep cycle.