Roger Calvert wrote

I have been looking at the split files. The bounds are, as you say in 
your explanation (1), adjusted slightly. For example, latitude 43.0 on 
the original tile becomes 43.06 on the split tile. This occurs on both 
tiles, so the lower tile will gain 0.06 deg in which it has no data, and 
the upper one will lose its data in this gap. 0.06 deg of latitude is 
several km, so this accounts for my gaps.

I think you report problems that are long fixed now. What version
of splitter are you using?