I just started poking at this yesterday but I didn't have a lot of time to make it exhaustive for you.
But I formatted a new blank disk on my 2000 and dragged over an ADF of Cannon Fodder (labelled as the UK version) for Disk 1. That alone took some time to do. I got an error at the end of the copy claiming the disk couldn't be verified or some such and the icon on the desktop showed NDOS.
Then, I booted my Amiga 1000 with a Rejuvenator up with this disk in the drive.
It booted just fine and marched all the way through to asking me for Disk 2. I never got to Disk 2, but for the few screens I did see everything looked totally fine.
The rejuvenator I'm using has 2mb Chip and is hosting an original A3000 Agnus. Other than that, it's all the same as yours. (Well, and it has a RAM expansion, too.) The only real difference, though, is the Agnus. I should be able to make more disks later but my initial test on this machine looks fine.
Remind me - is your A1000 100% stock? Do you have the front expansion RAM, Fast? Anything else or pure stock?