I'm not an expert, but if all you're looking for is a reasonable explanation of how we could get billions of species in a few billion years' time, it's best to understand that what we have is an exponential problem. Say we start with one species, and every ten million years it splits into two, and each subsequent species also splits in two every ten million years. Of course in the real world there are limits to growth, and sometimes a species will go for more than ten million years without speciating and sometimes take less time, but this is just an example. Anyway, after 100 million years you'd have 2^10 or 1024 species, at 200 million years you'd have 2^20 or 1,048,57, and at 400 million years you would have 1,099,511,627,776 species. So at any "average" speciation rate of ten million years or less, and span of time greater than 200 million years, the thing keeping the number of species out of the trillions digit is going to be environmental limits, not an inherent inability to get that much diversity that quickly.