Answer

I wasn’t familiar with it, and it is definitely interesting.
At first I thought this is not a matter of the heap paradox but of the infinite. After all, the last epsilon is as small as you like, so there is an epsilon here equal in value to a perutah, and in the limit as it goes to 0 it is not less than a perutah’s worth but literally zero. (If you assume there is always a hundredth of a perutah here, you can still divide it and say that this still isn’t it but only half of that, and so on.) This raises the question whether an epsilon as small as we like is identical to actual zero or not. (An epsilon is a tiny segment, so its dimension is 1 and its length is 0. A point has dimension 0 and no length.)
Although with hammer blows this is of course not continuous, and each blow has some finite value. The question is whether it really means actual hammer blows, or whether that is just a manner of speaking for the value of the completion of the work; in that case I would still be right.
It could also be rejected on the grounds that for a gentile, less than a perutah’s worth also has value; the question is how much less. But something infinitesimal has no value even for a gentile. Here, of course, the question of the heap arises: from what point does it have no value? This reminds me of what Rabbi Ben-Zion Abba Shaul said when he was asked whether it is permissible to drink water from the Kinneret on Passover because of concerns that someone may have thrown in a piece of bread (where even the tiniest amount of leavened food is forbidden). He answered that even "the tiniest amount" has a defined measure. Very nicely put. By the way, here the solution is clearly as I said: the value is proportional to the size of the epsilon, and not dichotomous—either it has value or it does not. And it requires further inquiry whether value in a person’s eyes is in fact dichotomous: either he assigns value to it or he does not—what is important enough in his eyes. Or perhaps that too is a heap, and the cutoff threshold is only legal-halakhic.