Reducing complexity by the factor 100 doesn't change much. I reduced the number of 10^120 games by very much more, 10^60 for my argument. And even with this bold assumption and the even bolder assumption that Moore's law will hold for so long, we see it takes at least two centuries. Fwiw, I believe chess will never be solved completely for the reasons Jesse stated. I.e. we will never be able to give an optimal strategy for every position for both players.
And it's difficult to judge what a 'logical' continuation for a certain position is. For example Kieseritzky might have found most moves white made during the
Immortal Game quite illogical, but still lost it.