So I've now deployed this site to Heroku. It was all pretty easy. A few things to muddle through, and a few things that Heroku expects to be a certain way, but its all easy enough to sort out and fix up.
I also managed to convert from Sqlite3 to Postgres. This was fairly
easy once I fiddled with the SQL, turning some ones and zeroes into
trues and falses, and removing the SQL that manage.py migrate will
already have run.