But you're right there is some more tinkering that needs to be done.
Clearly there have been one hell of a lot more the 350k species. An extra input assumption you need is the average duration of a species. This could be a bit tricky even to define over time since one will frequently blend into another. But why not pick a number as a starting point. Call it 1 million years (seems high for beetles but I've read the 5,000,000 is the average for larger animals).
Remember that life is a bush of species. So once you have a new twig (species) you get a new opportunity for a branch. I think that means that if you get to 10,000 species you want to ask how many of them wil l produce a speciation event per year.
I would say that the rate of a new species arising from one species every 757 years seems high (though critters like these seem to be able to speciate in decades) However, as noted above, we aren't dealing with one species once we get going.
Let's look from the current diversity forward , how many new species may arise from 350 K species in a set number of years? How many have to speciate to maintain diversity if we all 350K of them will be gone in a million years? We need 3 new species a year don't we. But this one has to arise out of 350,000 species.
Continueing to think out loud: That suggests a speciation event from one in 100,000 species each year will do it. That seems to work out to an event from 1 species each 100 kyr period which is plenty long enough right?
This is fun! But it is going to take a lot of reworking to arrive at anything which makes any sense at all.