To build off of Bob's idea, we could also do it like Formula 1 qualifying. This would have basically 3 structured, time-limited periods to submit your times (the time-frames given are just examples). Here's how I see the whole system working:
Once the RPC is decided, we immediately move into the first of the three periods for time submission. The first being the longest (backwards from F1) in order to allow people to get used to the car.
Period 1 - 3 weeks:
First, you get as many tries as you want to perfect your time. Then, once you're happy, you submit that time (only 1 submission allowed). After the 2 week period is up, we have a temporary leaderboard established.
Next, we eliminate the bottom 30% of the board, and their times are set in stone. If you didn't make the cut, dealwithit.gif and be happy you at least participated and had fun!
Your time will remain on the leaderboard, but you can no longer improve it.
Period 2 - 2 weeks:
Now, you made it to the next phase. Again, take as many tries as you want to perfect your time even more. When you think you have a nice time, submit it (only 1 submission allowed). After the 2 week period is up. We cut out all remaining times except for the top 10. It's now on to the final battle for the top spot.
Period 3 - 2 weeks:
Now, normally in F1, this final qualifying session is longer than the previos 2, but I think doing it backwards and having the first one be longest, and the final session shorter would work better since those who are eliminated really don't want to wait ages for these last 10 guys to battle it out. Again, you take as many tries as you want, and make your one-allowed submission for this period and hope for the best.
The 2 weeks goes by and the final leaderboard is determined with the winner.
This system would give people their "extra" chances if they feel they weren't good enough, and is less harsh than the only 1 submission Top Gear style dealwithit.gif.
At the same time, it's not TOO easy, since if you place in the lower 30% initially, you're out of it for the remainder of this car's time scale. This also prevents some random guy who placed last initially from getting a re-do and coming out on top.