Thanks for the tip @quietbadger27. I have tried to regenerate initramfs, but it complained about (infamous) lack of space (thanks a bunch for the tip! Nothing further couldn’t be done without that!), so I cleaned it and succeeded to regenerate it but to no avail again. Couldn’t pass the grub screen with the same error messages stated above.
Meanwhile, I have tried to recover qubesd service. I have finally traced it (service by service) to the first missing point:
libvirtd.socket: Failed to queue service startup job: Unit virtlogd.socket not found
Since I always keep a copy of dom0’s /etc and /usr directories in a user@dom0 too, not only in other VMs/external drives (yep, I know I am smart 
), I have just copied backup of /systemd missing files into /etc/systemd, manually enabled and started service by service, finally to succeed to recover ‘qubesd’ service. That of course didn’t resolve f41 missing entry.
But I got an idea. I booted f37 now fully working entry, and all I need to wait for was… a new kernel update, in this case 7.0.12 from the current-testing repo.
Ran sudo qubes-dom0-update --action=upgrade first, just in case to get new kernel.
After that, manually ran STAGE1-3, only smoothly to pass it with an updated kernel, which now caused proper rebuilding of the grub and regenerating initramfs, and after reboot, here I am writing from 4.3.1 f41!
I will not mark any post as a solution, because it was rather a complex process, with the much appreciated helpful tips from many of you guys. I will edit topic subject as [solved] instead.
So, as usually, at the end of the day it’s not about
… but about being or not in the know!
Cheers