Ok, that's fine. I am reconsidering the whole thread on the basis of
some further looking.
Your original observation (citing uninformed comment) was that although
UK "soppy" and US "sappy" were more or less synonymous, they were not
mere dialect variants, but had separate histories. I think this is
correct. "Sop" and "sap" are not from the same root, at least as far as
Watkins is concerned. However, they do both refer to...um, juicy things,
and I think that they have traveled the same semantic pathway to arrive
at the sense "overly sentimental".
On the basis of a hasty consultation of Wentworth and Flexner
(Dictionary of American Slang, 1960), I said that USEng "sappy" did not
have the "sentimental" sense. I was wrong. (W&F probably just missed
it.) This sense is given both by my AHD (1973) and by the current M-W
online.
Also, UK has "sappy" for "foolish" (citations from 1670-) and "sap" for
"a fool, simpleton" (1815-, which they say is a shortening of "sapskull").
To tabulate:
"soppy" = "sentimental" UK + US
"sappy" = "foolish" UK + US
= "sentimental" US only