Yes I agree with your thought that the early wake up is likely linked to being OT at BT. You can't always avoid these things so don't beat yourself up over it. The routine is pretty much perfect!! Look at those times!!
Again with trips out, you can't always avoid going out.
I avoided most things which didn't fit around naps because for me the most relaxation I could get was when mine was asleep in his cot. When I tried to go somewhere at the wrong time he didn't sleep, just screamed, I did try to get him used to it but in the end I preferred the calmer routine and doing less. Mine would eventually sleep in the car seat if I left the house at the right time which gave me some level of ability to get out although I still had to time it.
I don't know how other people who are out and about during maternity leave do it.
Honestly I think most people struggle with something or other but it's not necessarily seen from the outside. Most of us look like we are managing brilliantly when actually we are exhausted.
During my DS's phase of 40 min naps I would put him down in his bed at home for a nap and then run around the house like a crazy woman getting things ready for when he woke, packing a bag and getting the sling on me, then I stood by his bed wearing the sling a few mins before 40 mins so that the second he woke I could get him in the sling, pick up my bag and leave the house. Walk him in the sling to my car (a block away), get him in, drive to the park, get him out and back in the sling, walk as fast as I could to a bit of grass, lay out a blanket and put him down. Then change nappy, feed. Stare at the trees for a few minutes, get some fresh air, look like I had all the time in the world, look like I had a perfectly happy baby who never cried... but my eye was on the clock and I had to time our trip back perfectly to avoid the screaming melt down. We only had an hour at the park, if that. At one time I had to make sure we were back in time to get him in the cot for the next 40 min nap, at another I knew I could get him to nod off in the car if I was driving at the right time but then I had to sit in the car until he woke, in those days he wouldn't transfer from car to sling or sling to cot. At another time (older and heavier) I'd managed to get him to a point where I could transfer him so he could nod off in the car and if I spoke constantly to him I could lift him from the car into the sling and transfer him - which meant carrying a heavy baby plus bags a block or two from the car then up 3 flights of stairs to his bed before I could put him down and tell him to stay asleep! I was always exhausted but from the outside it looked like everything was a breeze.
I'm not saying I had it worse or better than anyone else, only giving an example of how it can look wonderful from the outside when really it is very very hard. You're right it's not sustainable but babies get older, things do generally ease off, the A times get longer and we get some of that Y time we all need.
Have you started solids now? Just wondering if you are offering solids in the evening? It might be something you can skip in the evening in case it's causing any gas or tummy pain during the night. Offering solids earlier on in the day can give them a good amount of time to get past gas etc before BT.