More hugs lovely
sleep is such a stress isn't it?
A couple of things jumped out at me from what you said, just clutching at straws but will share in case any of it helps. You deserve your sleep!
First one was when you said if she fell asleep late for nap you cap nap and do later BT. For us that's always a major error, we never move BT later, only ever earlier or J gets OT and struggles to settle. So if set BT is 7pm, I would always cap nap short enough so that I could put her down for 7pm and she'd be tired enough (not that I get it 100% right.....) to sleep. So if she falls asleep between 1.30-2 I generally wake her at 3, if she didn't sleep until 2.30 I'd let her have until about 3.15 but no later. On the odd occasion she's slept really late e.g. car nap at 3/3.30pm I make it a short catnap only. And if she's shattered we have the option of bringing BT forward, but not pushing it later.
Second one was about set nap being a joke because nap length varies so much. My understanding of set nap was not that it's a set length, but that you put down at the same time. So the time the nap starts is theoretically the same, but some days LO will take a shorter nap and some days a longer one. Some days she'll take longer to fall asleep, same at BT, but nap and BT are still 'set' if you see what I mean. If she really needs it on shorter nap days you bring BT forward. If your gut tells you she's OT by BT most days though, then perhaps your set BT needs to be a bit earlier?
If she's in her bed chattering and not falling asleep does it worry you? Other than the fact she might be OT or UT depending on exactly what she's doing, we've had much more of this in recent months whereas usually J was like your DD and would be straight out if I get the timing spot on. To be honest I've given up on trying to work out which way wrong I've gone! So I just accept that she's in her room having quiet time, and I get on with eating lunch/doing jobs/having some quiet time for me. Could you do that?
My only other thought was perhaps she gets into a bit of an UT/OT loop spanning a couple of days? I think this is what happens with J. So it's not uncommon if J has a good nap (1.5h for us) followed by a good night, that she will either take forever to fall asleep for nap the next day or not nap at all. I'm guessing because she's had enough/more than enough sleep. But then obviously next day is OT from the NND. So it can be a bit of a wonky nap day and take us a couple of days to get back to a 'good' nap. And then we go round again.
Wish I had a magic wand and could sort it out for you though hun, I'm sorry if none of my thoughts help xx