Soap on a rope

"How do you spell 'rope'?" A.
"R-O-P-E?" Me
"I thought so, but then I thought of "soap" and got confused." -A.

Well, once she brought up the subject (and we brought up a lot more rhymes), I tried to research why "soap" is spelled differently. It comes, apparently, from the ME "sope" and the OE "sapa," with ties to some Germanic "seife." "Rope," in contrast, apparently came from ME "rope" and OE "rap," with ties to Germanic "reif." I can't figure out why soap developed an -oap instead of an -ope. It must have to do with that stray E on the end.

I need an Oxford English Dictionary. And a degree in linguistics...