The comparison between the “heap of sand” analogy and “absence of pain” is interesting. Would you mind explaining it a bit more?
The central issue is what is the sorites paradox/syllogism in the first place. Some of this is contained in DeWitt's reference quoted here.
But contrary to the view that the point is that the sorites method of argument is an absurd request for an arithmetical rule on things that everyone understands, I would say that the point is somewhat different.
Words like "heap" and "good" are useful even though they have no mathematical precision, but it needs to be understood that these words lack not only mathematical precision but any intrinsic meaning of their own absent reference to the individual items that are being described in summary.
Epicurus is arguing that "pleasure" as a concept has no meaning apart from the individual instances of pleasure which are contained within the summary term. Of course the concept is very useful as a way to communicate ideas, but Plato and the others are asserting that there is an absolute realm of ideas where there is a "perfect" or "form" of pleasure, and that pleasures are pleasures because they somehow mystically partake in this form or idea.
"Absence of pain" is something similar - it is a concept and not an individual experience. The individual experiences are two - pleasure and pain. Denominating something as "absence of pain" is useful, but in this paradigm "absence of pain" means exactly the same thing as "pleasure" because there are only two possibilities. But not only does "absence of pain" as a concept mean nothing in itself, the rest of the chain is to observe that "pleasure" as a concept means nothing in itself apart from individual instances of feelings of pleasure. The search for "absence of pain" means nothing more or less than the search for "pleasure," and both of those words in quotes mean nothing more than real feelings of real beings at particular times and places.
I would argue that as a concept the word "pleasure" is useful to describe the goal of life, because you need to describe the goal of life in words different from or "virtue" or "piety" or "nothingness" depending on whether you're talking to a Stoic or an Abrahamist or a Buddhist/Hindu. But using the word "pleasure" in that conceptual way is not a full description of a particular experience by a particular person at a particular lime and place. For that you need words like "sex" or "drugs" or "rocknroll" or "resting" or eating or drinking or sleeping or reading philosophy or even simply reflecting on your good memories or expectations.
Likewise you could say exactly the same thing as said in that last paragraph about "absence of pain," since in a system of only two options, absence of pain always means pleasure. But there's another important use for the term "absence of pain" -- to refer to period of time when ALL of the experiences that a person is feeling are pleasurable and not painful. "Total" absence of pain would mean that in that time period you're looking at there are only specific pleasures, and no specific pains, and thus that circumstance cannot be improved. Yes "total absence of pain" is a very broad concept, but it is a concept that describes "the limit of pleasure" -- it provides a description of a situation that cannot be improved, and if you are interested in philosophical arguments (not everyone is) then you want the term "absence of pain" so you can have a definite description of a condition that fulfills the requirements of the logicians. They argue as did Plato and Seneca that in general philosophical terms, something that can be made better cannot by definition qualify as THE good or THE goal of life.
A life in which pain is absent is a term that gave the Epicureans in the past, and us today, a logical description of "the best life" to which we all should aim. We won't succeed in eliminating all pain from our lives any more than Epicurus did. But it's important for those of us who want to have a clear idea of the goal that Epicurus was talking about. And it's important to be clear about the goal not only so we can live better ourselves, but so that we can prevent the Stoics and Buddhists from trying to turn Epicurean philosophy into a tool of their own mistaken ideas.