Hi there - so much sympathy. Another one suffering from the ongoing '4 month' sleep regression here. Our DS is 5.5 months, and I was totally unprepared for it, as my DD was an amazing sleeper, and (in the rosy-tinted fog of memory) am pretty sure she was sleeping thru pretty consistently by 6mo. Just wanted to add another voice to the affirmation that you are NOT failing as a mother. There is so much guilt and mother-judgement around sleep, but I did exactly same thing with both kids, and our experience is so different for each. DS has always had a really sensitive tummy (very cry-ey newborn, due to difficulty pooing, etc), and that has consistently affected his sleep too.
I was on my knees a few weeks ago, and the only thing that has helped me has been relentlessly collecting data. I knew something had to change and wanted to try some very gentle 'training' or just some other tactics really, as what I was doing (feeding to sleep every wake-up) wasn't working for me - and didn't seem to be helping him much either. I knew that he wasn't hungry, but was using the BF for comfort, and as a sleep association. I wrote down every wake-up and tried to see a pattern. What I came up with was that, following the bed-time feed (7pm) most of the subsequent wake-ups were due to wind. So, if he woke 8, 9pm, etc, I would try just to get the wind up, and re-settle without another feed. My goal was to feed at the dream-feed time (10.30/11pm) and then hold off until around 3am. So far, this is mostly working - and I have got my husband to do all the wake-ups between 10ish and 3ish. Picking him up at that point seems to make things worse, so we have managed to get him to a point where he will resettle simply with stroking head and tummy, and giving the dummy. Dummy is the magic bullet at that time - as he's such a comfort sucker. He had never taken it much before, and never during day sleep, but at night it seemed to replace the breast at those crucial wake-ups. I think when I was feeding him every 1.5/2 hours during the night, it was actually upsetting his tummy, and making him wake up more often. To be honest, he's still waking up far too much, but at least I'm not locked into feeding him as often. And, if your DH can settle him - there's the opportunity for a 4 or 5 hour stretch of sleep.
What has helped most with this regime is that even though it's far from ideal, it has become really predictable. I settle him myself up to 10.30ish, but ONLY ever feed him 10.30/11ish (or closest wake-up) and 3am (or closest wake-up). Of course, all of this is predicated on the ability to settle him, and I think we're possibly lucky on that front, in that he's taking the dummy. But, just wanted to share in case there's anything at all that might be of use in our approach.
Also - he was crap at day sleep right up until 4.5 months, then started doing longer sleeps. This was also when his night sleep packed in, so he's not like most I read about, where it all goes pearshaped at once. BUT, what I have taken from that is that - they do things when they're ready. I'd tried extending his day sleeps from their clockwork 45 minute duration for AGES. Did PUPD, etc, but nothing worked. Until, magically, he did it. I am hanging on to the possibility that this will work with the night too.
Anyway, apologies if any of the above is irrelevant or argh-inducing. Sometimes I hated other people so much if their baby was doing anything that seemed marginally easier or better. You will come out of the fog. I have insomnia too, so know how the pressure to sleep can be counterproductive (I often feel like my brain is my worst enemy). When you're in it, it feels like nothing will help. Try to be as kind to yourself as possible; and rant as much as you need. Sorry for the epic post. Thinking of you.