I hate to admit this, but you seem to be right. My mistake was that I did not allow for the fact that when you pay, the stake you are risking gets reduced by the amount you have paid.

This leads to bizarre follow-ons... for example, you should pay only half as much to remove the last bullet (1/6 --> 0/6) as you would to remove 1 bullet from 4 (4/6 --> 3/6)... and you'd pay 6 times as much to remove the first bullet (6/6 --> 5/6) as you would to remove the last bullet (1/6 --> 0/6). Which incidentally contradicts the original version of the paradox as stated here:

http://catdir.loc.gov/catdir/samples/cam033/2002035199.pdf - page 11

That paper states that most people would pay MORE to remove the last bullet than the first, but the right number should be the SAME in both cases. However, it does not account for the the loss of utility when you pay the money, and the subsequent lowering of the stake if you lose. So, the paradox is even more extreme than originally envisaged...!

Edit: and furthermore, under the assumptions made, you'd pay the same amount exactly to remove one bullet out of 6 (6/6 --> 5/6) as to remove all six bullets (6/6 --> 0/6), this amount being all the money you have plus debt to the point where life would hardly be worth living, so your utility is pretty much zero in any event... I guess this shows that weird assumptions lead to bizarre conclusions.