Running DiagROM's fastmem scan I found that only bit D7 of the lowest byte was faulty, all other bits worked fine. After a bit of SIMM swapping to rule out bad sticks of RAM, and a thorough connectivity test of the FastRAM data bus showed that everything was connected as it should be (and not obviously shorted to anything it shouldn't!) I turned my attention to the chip U891, which is a 74F245 bi-directional tranceiver connecting the lower 8 bits from the FastRAM to the Amiga bus. Here's the datasheet for the component: https://docs.rs-online.com/4604/0900766b80024d3b.pdf.

There was noticable corrosion around the pins of this chip from when the original Varta battery of doom vented it's wrath, but connectivity appeared to be fine, so I fired up my trusty Oscilloscope and probed the chip:

looking at both the faulty D7 and a randomly selected known good bit D1 for comparison. Here's what I found:

When T_R is high, and _OE is low, as occurs at the trigger point in the middle of the trace, this is when the chip is reading data from the RAM (pins D1_R and D7_R) and buffering it onto the A4000's data bus (bits D1 and D7 shown here). D1 should follow D1_R and D7 should follow D7_R.

D1 does this as expected (see green highlight above), but D7 immediately drops like a stone to logic 0 (see red highlight above) as soon as _OE (active low output enable) goes low regardless of what's happening D7_R (orange highlight)... which would seem to imply an internal short somewhere on this chip.

Off to my trusty electronics part retailer for a replacement 74F245,

One quick hot-air aided replacement, and...

Success!

FastRAM is now up and running!

At this point everything was looking pretty rosy in DiagROM. so it was out with DiagROM, and in with Kickstart (3.1 vintage in this case). and on to Kier Frasier's excellent Amiga Test Kit (grab it from here: https://github.com/keirf/Amiga-Stuff/releases):

All seemed well until I spotted this:

"WARNING: AGA Alice with bad Lisa ID"

So.... That's next on the debug hitlist!