Well, I have some news. I think I isolated the problem with the weird A1000 boot behaviour. I was testing it on a multisync monitor (which is an acorn-branded M1438) which syncs down to 15khz no worries. I had it for years hooked up to an A4000 so I could use the AGA pass-through to have whatever mode I want. Anyway, about 10 years ago the AGA output stopped working on the A4000 and then about a year later it wouldn't boot.
Long story a bit shorter, I'd given up on the A1000 and moved to trying to fix the 4000, finding that it seemed to hang around the end of the boot sequence (booting from 3.0 WB floppy and not much other hardware). It seemed suspiciously the same behaviour as the A1000, so I tried the A1000 on the TV and it booted and works fine!!!! Even the A4000 finishes booting through the TV although it seems the RGB output is fried (looks like I'll need another thread for that one).
So, it seems that the RGB-VGA cable I was using is defective! One step at a time, these Amigas are being revived :-D