I'd suggest you are not taking the correct messages from the communication baby is giving you. I can give you a couple of examples of this from your opening post:
Both things [rocking him or offering dummy] will settle him for a minute or so but then the crying will start again. Both things will settle him for a minute or so but then the crying will start again
Settling baby to sleep often requires some significant time and effort from you.
Giving a dummy (best answer, in my opinion) and/or rock and within 5 minutes baby is crying again, or maybe hasn't even stopped crying, this does not mean these methods are not working. It means you need to carry on trying for longer and hiving more help to get baby to sleep.
It might take 10, 20, 30 minutes of increasing effort to get baby to sleep. For example if baby wakes and it was only 1h or so since last bottle, I'd know baby isn't hungry. So would:
- give dummy and cuddle into the sidecar cot. Expect to need to gently hold dummy in for baby or reinsert it a few times. Maybe some shushing and my hand on baby's chest to settle in addition to dummy. I'd give this 10 minutes or so
- if not settling from the above after 10 minutes, pick baby up into a wind position (on shoulder) and rub back. Some swaying while baby is there. Hoping to get a few burps and some calming rhythmic movement. Give this 5-10 mins, depending on how successful winding is and if baby is still crying a lot.
- lie baby on my bed and swaddle (see below)
- if calming down from winding and swaddle, into cot and another 10 mins of dummy and hand on chest cuddles
- if still not calming, into cradle hold whilst swaddled and rocking whilst holding dummy in. I would probably just keep going with this until asleep, regardless how long it takes.
He has a strong startle reflex which doesn't help, but doesn't like being swaddled
Here is another example. On what basis are you taking the assumption he doesn't like being swaddled?
Fighting against the swaddle? Arching back? Screaming whilst being swaddled? Kicking legs? Flaying arms? All of these things are signs baby needs a swaddle, wants a swaddle even.
The swaddle is there to calm baby down when giving all these signs - there are all over tired signs. Screaming, flaying arms, arching back, kicking out - these are all communications that say "Pleassssseeeee please please help me go to sleep. Right NOW".
Swaddling, dummy suck, swaying and rocking - these are all things that help baby get there. They are not magic wands, none of them. But every one helps to get baby to be still, calm and quiet in order to relax and go to sleep.
Actual signs baby doesn't want a swaddle is that baby goes to sleep easily without it. So it therefore serves no purpose. If a newborn baby struggles going to sleep, put in a swaddle.
he wants to go back to sleep - but for some reason can't
A little unrealistic expectations here.
This is true of all babies. They don't just lie down and go to slerp sleep when tired, none of them. You have to help. Sometimes significantly.