Sorted!
The green screen was caused because this Amiga 3000 for some reason required all 2MB of chip RAM to be fitted. Not sure why, but there we go - I thought it would run with 1MB.
Once I fitted the other 1MB, the yellow screen came up again, which is correct without a Zorro backplane.
So, I attacked the backplane by desoldering all of the pin 53 and pin 51 pins on the connector sockets. Once I did this, pin 53 and pin 51 were no longer shorted, so I knew the fault was on one of the pins, not on one of the tracks. I then re-soldered pins 53 and 51 one by one until the short re-occured. I found that the offending pin was pin 53 on the socket next to the motherboard - then all I needed to do was to shove the soldering iron up between pins 53 and 51 by the edge connector. It melted the plastic bit of the connector slightly (I have a fine-tip iron, so not too bad) but it duly flowed the solder back onto each pin respectively! No short!
Plug it back in, and this is the result!

So: the moral of the story:
If you get a green screen on an Amiga 3000, it may not mean that the Chip RAM isn't working, it may mean that the entire chipset is prevented from working! You can tell this because the LED doesn't flash. Denise doesn't have a _RESET line, so will still work, hence the green screen - but without Agnus there's no LED flashing - just a green screen and then reboot, then green screen, then reboot.
If the _RESET line is held low (active) on the A3000, the CPU will continue running normally, because the _RESET line comes
after the _CPURST line on the reset buffering circuit. This is how come the Kickstart ROM was executed perfectly even though a reset line was active, and how Ctrl+Amiga+Amiga (_KBRESET comes from Gary and comes even before _CPURST).
With no backplane inserted, the screen will go yellow if all Chip RAM is good, it will go green if not.
Maybe this information will help someone in future, who knows...?
Expect this A3000 to feature prominently on YouTube videos shortly....
Edit: Forgot to mention; thanks for the pointers, those who helped
