Just for clarity's sake:
Legacy FF to Pale Moon : use cookie XPI (mega link in previous message - - if the XPI doesn't work, just edit the install.rdf to include the FF GUID)
Pale Moon to Legacy FF: use cookie XPI
New FF to Legacy FF: use FF Netscape Cookie to export from New FF, use cookie XPI to import into legacy FF
Legacy FF to New FF: use cookie XPI to export from legacy FF, and ???? for import into new FF (suggested: sqlite method)
New FF to Pale Moon: use FF Netscape Cookie to export from New FF, use cookie XPI to import into Pale Moon
Pale Moon to New FF: use cookie XPI to export from Pale Moon, and ???? for import into new FF (suggested: sqlite method)
On SQLite: overwriting the file would replace existing cookies, of course. An alternative would be to directly edit the sqlite db. I've used DBeaver to edit sqlite files in the past, but it's been a while. Again, worth a shot, may help edit the cookies db quicker.