Sorry I got distracted by the DC earlier but this was what I meant by giving myself "outs".
Basically any time I tried to commit to settling DC in their own rooms (by feeding to sleep then putting down) I would get frustrated and feel like it was never going to work and give up and bring them back to bed. So what I did in the end was give myself a target to aim for.
At first I tried to keep them in their own rooms until 11pm. And if I had 2 failed attempts to put them down in a row, or I counted 1 hour from the time that I first went into the room and they were still awake, or they woke up again less than 45 mins later, then I was "allowed" to give up and bring them into bed with me. Some of these rules ended up being redundant or I increased the requirements over time once I became more confident about being able to make it.
That just helped me to keep going and not give up too easily - when I could look at my watch and think OK - I'll just try another 15 minutes, or whatever, then it would feel achievable whereas keeping going for the whole of the rest of the night felt impossible and I might as well not even try.
I surprisingly found a lot that the point I was about to give up, when I did then realise I only had to try for another 15 mins, I was actually successful in putting them down again. Whether it's that I was simply prone to giving up just as something was about to work, or whether it was that I was really stressed and sending out some kind of stressed/desperate "vibes" and then I relaxed once I knew I didn't have long to go - I don't know.
In order to commit to my new plan I found some things to do on my phone to keep myself awake during the bits where I was sitting in their room trying to settle them. The most successful I found were simple but addictive games without too many ads - City 2048, Drop The Number, Solitaire and Suika Game were the some which worked for me. Or trashy formulaic novels - I would read things like Cathy Glass, or old childhood book series I had loved - if you google "Read XXX free" you can often find websites where they come up for free (try using an adblock browser just in case). It has to be unfamiliar enough to scratch an urge to see what happens next but easy enough to process when your brain is running on zombie mode.
I did this with the first two DC around age 2.5, but I did it with DC3 around 16mo (newly putting him into DC2's room) and it worked exactly the same, so I didn't need to wait. It did take longer than "standard" sleep training but I also wasn't comfortable with that so I was OK with it taking longer. It was knackering, but I was knackered anyway so it didn't make a huge amount of difference there. And once I was getting some chunks of sleep in my own bed without DC constricting my movement this also did help a lot.
First thing to establish if you haven't already is getting DC to do the bedtime-to-9:30 stretch in their own room - this is completely non disruptive to your own sleep so it's a nice easy first step. From there, the rest of the night can then go in chunks so maybe aim for 11pm as a goal, then midnight, then 1am, 2am etc. IME I didn't have to go past 2am - once I started aiming for 3am, they just slept through or at least MUCH better than before. And TBH once I got to 1am and once they got used to the concept of feeding then being put back into their cot, they also stopped waking up as often.
Lastly I know you said you feel better when they sleep through so you think it's not iron (or similar). And I do get that, but I also think that when you have a non sleeping DC and they sleep through - it feels amazing because it's different. It doesn't mean you're not deficient in iron, and if you are then it will be making this all so much worse. It is worth getting the blood test if you possibly can, because if you get it medically confirmed you can justify taking the massive iron supplements, which are dangerous to take if you're not iron deficient. If you don't have the spoons to make a GP appointment, then do try a nursing/pregnancy/women's health multivitamin at the very least. It can't hurt.