Ok. I *think* I've found the issue.
I was experimenting with the guard terminal and saw some very strange behaviour where the output voltage actually increased when using the guard terminal and adding a load, that really didn't make sense to me, so I began to look at the output switching to see what was going on.
With remote sense off the 4000A should connect the sense lines to the output lines, however I wasn't seeing continuity on the low terminal (high was ok), and looking at the DC PCB schematic it looked like one of the relays (RL12) was most likely the culprit.
However on further inspection it was actually a fuse (F5) which had blown. This is actually in the power output path so it's surprising that there's any output at all, so there must be some path via GU or GU TERM (which I'm hoping explains the previous weird guard behaviour.)
I don't have any 1A PCB fuses and I didn't like the idea of using a 5A one just in case there was another issue, so I bodged in a 500mA cartridge fuse on some longish wires just to test it.
Initial results are good, in remote sense mode, I see absolutely no drop with a 100K load and just a few uV into a 10K load, a 1K load still shows a fair drop (about 100uV), but I do have the long wires and am seeing a significantly higher resistance through the wires and cartridge fuse than the datasheet for the pcb fuse shows, so hopefully this will be better with the proper part.
So I'm now waiting for the part to arrive and will then test again.
On the four-wire vs. two wire difference ... given the setup, the only real difference is internal to the 4000A, so wiring from the terminals via the motherboard, to the DC board and relays ... is that what you are talking about? If so, then that makes sense to me (no pun intended!) Externally the meter is parallel to the load and doesn't share any of the path (other than through some banana plugs for the purpose of this test) so I don't see how that could make so much of a difference.