Well, SQLite has internal hooks for compress() and uncompress() so I would like to use those. I just don't know how.
From the documentation, it seems I would need to call

$dbh->sqlite_create_function( 'compress', 1, sub { # magic incantation
+s for compression } );
$dbh->sqlite_create_function( 'uncompress', 1, sub { # magic incantati
+ons for uncompression } );
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Then when I call INSERT or SELECT I need to compress() and uncompress() the text strings.
Maybe I could use IO::Compress::Zip for the magic incantations...?
That's what I can gather, but I can find no specifics on implementation.