If you don't want to just use Sqlite (understandable), and you don't want to write something that is as good as Sqlite (also understandable), then you're going to have a crap database implementation. There's just not a lot of other options there. Jonas' comment just reiterates the lack of choices.
But given the three bad choices, the question does arise: Was IndexedDB really the best of a bad lot? In 2009, a lot of very optimistic things were said about IndexedDB performance, adoption, usage on mobile, developer acceptance. It's been 6 years, and I think it's safe to say that IndexedDB hasn't lived up to anyone's hopes.