What is your brewing setup? I've used your grain quantities in BeerSmith with a Braumeister 20L setup for the out of the box efficiency (without stirring the malt during mashing or a finer grind or extra boiling) and it gave me a post-boil of 1.042, which seems to fit with your result so I'd guess you had an efficiency issue. How did the mashing go?
I've noticed that when boiling for the standard 1 hour, I get about a 10% increase in gravity (for the digits after the 1 - that is, pre-boil of 1.064 leads to post-boil of 1.070 ish), so in your case 1.037 to 1.041 would check out for me.
For my brewing setup, 30 minutes at 63C doesn't really cut it, I've tried it and noticed 60 minutes or even 90 minutes work way better. But then I mostly use kveik and the indication seems to be for longer mash times (something about it being unable to digest sugars made of 3+ units).
I'm not sure I get your last point. If your FG is higher than expected, you should reasonably have more sugars left over from fermentation, so more residual sweetness.
Regardless, I'd suggest RDWHAHB, and see what you get out of this. Do share your final results, I am curious what it's like.
Out of lazyness, I just let all my beers sit in the fermenter for 2 weeks and that seems to work out just fine. Some finish bubbling after 2 days, some after 12.
Edited to add: just noticed from your yeast link, you also use an all-in-one system, does it suffer from the same low efficiency issues as the Braumeister, I wonder?