My first try took me 17 days, my second try took me 13 days, and my third took me 4 days. On day 3 i got really lucky because i hit like 30 platforms (not lying) so i was pretty high, made lots of money, and made even more money because i was in the air for probably 3-4 minutes and i made 10,000-15,000 then i bought e-rockets, reduced my fuel consumption, increased my launcher, and increased my bands elasticity.
I can't be bothered going for four for the moment, though it's certainly plausible. So I stuck with six.
Basically all you really need is $16000 to completely upgrade your launcher.
That said, though, it's almost certainly as fatal as Verne's original idea :P Given that not counting air resistance, the hedgehog would have to be travelling at about 11km/s (28000mph) by the time it left the catapult. And that's one heck of an acceleration...probably somewhere in the order of 1000g...