Peter, I am no expert on electronics but I do like a challenge. It may be worth checking a couple of things.
1) I agree trying to read an analogue volt meter is very difficult and they are not very accurate anyhow so suggest you measure with a DVM the actual voltage the meter is reading. If this is around 12.00 then that may be your answer if the low voltage alarm is taking the reading from the same source.
2) Whilst a 0.25v drop between the battery and the panel may not seem very much it could be significant depending on the conditions under which it was taken. If the load going through the panel was light ( less than 1 amp) then this would be quite a large drop indicating a high resistance somewhere between the battery and panel. Suggest you measure the drop with minimal load going through the panel and then repeat with a maximum load by switching on as much as you can – nav lights, fridge, chartplotters etc. if the latter gives a larger voltage drop than the former this would confirm a high resistance somewhere. I would have thought the voltage drop even under a moderate load should be less than 0.1v
Hope this helps