Since sqlite is local to your application, you can just bundle a newer version.
Speaking generally, if the Debian version is the way to go, the easiest way is often to grab the source package from sid and build it. It's literally just one command. Sometimes new dependencies will cause trouble, in which case some manual tinkering is required.
I've gotten some good mileage out of sqlite-utils[0] lately. It and it's parent project datasette[1] are a wonderful contribution to the sqlite community.
For example, deleting a column is a pain in the ass.
A single purpose script "rename_column.sh" would be nice, which combines all necessary steps and gives some guidance regarding edge cases.