Well.. I found the cause of the mysterious magenta boot screen!
One time when my A4000 managed to boot, and it was sitting on the insert disk screen, the screen suddenly went magenta again.
But what was weird was that the screen then filled with white lines.... but I could see the insert disk screen in the background!
I quickly checked Alice's temperature, to see if it was hot, and... the lines disappeared!
Let go of the chip... lines return. Press on chip, lines go. Hah!
One quick reheat of the chip with the Aoyue SMT rework station, and the problem got worse - black screen with bad sync.
Not giving up, I took Alice off completely, put a bit of fresh solder on some of the pads, put Alice back on...
Bing! Machine boots! First time! And second time! And every time for the last 30 or so attempts.
So if your A4000 doesn't boot, and you get sporadic booting with no obvious symptoms, just maybe you just need to resolder a custom chip or two.
Hurrah! Now I think I'm going to find a heatsink for Alice.....