Hi there,
First off, big (((hugs))) for what must have been a terrifying and very difficult first four months of his life. I'm very happy to hear that he now has a clean bill of health. What you've been through and continue to go through is obviously exhausting and I know there is always the temptation to let a LO cry when you feel at your wits end, but I assure you it is doubtful that would help your situation and would likely cause more trauma to your LO. He's already had a rough start to life. Shh/pat and PUPD are methods of teaching self-soothing and aren't coddling at all IMO when done correctly. If you are very consistent in using them, they work (not always overnight, but they do work).
So, I think your biggest issue here is that LO is in need of consistency. You mentioned that he needs his paci, but also that sometimes he hasn't had it. PUPD and paci don't mix, so I'm assuming the times you've tried PUPD is when he hasn't had it? It sounds like he maybe has a bit of a prop issue with the paci in the MOTN, but he transitions through naps without it, so I don't think it's something you have to get rid of.
As for routine, it looks about right for a 5 mo old, with some naps a bit wonky still. You should be aiming for about 2 hr - 2 hr 15 min of A time. The one thing I notice is that after a short nap, his A time isn't always reduced. If he does less than 1.5 hr nap, I'd pull back on the next A time by 15-30 min depending on how short the nap was. This should help hinder OT and hopefully perpetuate a longer nap the next time. Ideally at this age you'd like two full naps and a CN. The other thing to try to aim for in routine is as close to a 12 hr day as possible. So if he wakes around 6-6:30 am, BT is ideally 6-6:30 pm (7 pm at the very latest).
Finally, how are you feeding him. I noticed a BF in there, are the bottles EBM or formula? I'll try to get some feeding eyes on this for you too. It seems like he's having lots of little feeds, which is likely not helping the NWs. Obviously, he may still be adjusting to being fed at intervals than continuously.