While that undoubtedly sounds very impressive, IMO tests should not be what you use to ensure that your software is correct — in my opinion, they can be actively a bit harmful by giving you a wrong impression of correctness. Just take a look at https://www.sqlite.org/changes.html — after the recent 3.8.0, there were 2 bug fix releases separated by 3-4 days (!), with bug descriptions sounding relatively, hmm, trivial,…
But is possible to create very serious bugs even with high level languages, and proving software in a way to provide good coverage is extremely hard.
Having said that, if you have the choice, it's still unwise to spend huge amounts of time writing+maintaining tests but then balk at the relatively short amount needed to use a strong type system. It won't catch lots of things, but it will catch quite a few. For the limited concepts it can express, it can ensure correctness more rigorously, easily and quickly than any testing can. Might as well use the easy method where you can, right?
But sqlite is old and extremely portable - the only language that springs to mind would be C++. And while that does provide advantages, it's a bit of a stretch to claim those would merit a rewrite.