Most obviously, we could say that the paradox does not apply to VNM agents, since the VNM theorem assigns real numbers to all lotteries, and infinity is not a real number.

That works.

A fair coin is tossed until it lands heads up. The player thereafter receives a prize worth min {2^n · 10^-100, L} units of utility, where n is the number of times the coin was tossed.

In this case, even if an extremely low value is set for L, it seems that paying this amount to play the game is unreasonable.

I don't think removing the "like 1" helps much. This phrasing leaves it unclear what "extremely low value" means, and I suspect most people who would object to maximizing expected utility when L=1 would still think it is reasonable when L=10^-99, which seems like a more reasonable interpretation of "extremely low value" when numbers like 10^-100 are mentioned.