I checked out your dictionary link and Washington Post link. Neither of them mentioned the 25th of December. This entire three days sub thing after the solstice is astronomical fiction.
The only thing I found about the suffice -stice is from wiktionary that says it’s the proto-Germanic word for prick/sting/stitch.
https://en.m.wiktionary.org/wiki/stice
I don’t know if that’s what you’re looking for. There is no pagan celebration on the 25th, moderners made that up to attack Christmas.