Sympathies with the problem of cost. There are plenty of ways of slimming down the size of your datanbase by refactoring it. However, if you really have run out of ways of keeping it below the 4 Gig limit, then the most obvious choice is PostgreSQL. However, the syntax has quite a lot of differences from SQL Server, and this is going to cost a lot of effort to migrate the application.
Can you split the database into logical parts that can be put on different SQL Express servers?