We will first deal with the question of whether it is really forbidden to eat such food on Pesach.
Since there is no way of determining how much chametz residue emerged from the pot’s walls, we are required to assume that the entire volume of the walls was full of chametz and that it all came out during the cooking.[2] Since the volume of a pot’s walls (including its bottom) is always more than a sixtieth of the food it holds, we cannot assume that when the food was cooked in it, there was bitul[3] before Pesach based on volume. However, when food is cooked in a pot and one does not remember when the pot was last used, Halacha allows one to assume that the pot was eino ben yomo (had not been used for 24 hours) from its most recent use.[4] In that case, what comes out of the walls of the pot gives off a negative taste (noten ta’am lifgam). Therefore, even if the pot was not kosher, kosher food that was accidentally cooked in it remains permitted.[5] If one prepared pareve food in an eino ben yomo fleishig pot without intention to eat it with milchig food, he may afterwards eat the pareve food together with milchig food.[6] Cooking food in a chametzdik pot without intention to eat it on Pesach is a roughly equivalent case, and food cooked in an eino ben yomo chametzdik pot would thus seem to be a candidate for bitul. However, there is a machloket regarding whether it is permitted to eat noten ta’am lifgam of chametz on Pesach,[7] and the Rama[8] is machmir.
The Rama’s stringency regarding negative taste in a mixture relates only to eating the food on Pesach itself. On the afternoon of Erev Pesach, despite the Torah-level prohibition against eating chametz at that time,[9] the regular rules of kashrut apply, and the chametz from the pot you describe is batel.[10] However, since your question applies to all of Pesach, we must deal with the question of whether the change of bitul rules during Pesach itself transforms a mixture whose chametz was batel before Pesach, based on the more lenient pre-Pesach rules, into a forbidden chametz mixture when Pesach and its stricter standards begin (chozer v’nei’or).
The Shulchan Aruch[11] prefers the lenient opinion, that those foods whose chametz elements were already batel before Pesach remain batel on Pesach. The Rama[12] rules that it depends on the type of bitul that is involved. If there is no effective intermingling, and the bitul before Pesach was based only on lack of recognition (i.e., the chametz element is intact, we just do not know where it is), the food becomes forbidden when Pesach starts. However, if there is a physical mixture (i.e., the foods are mixed in such a way that the chametz does not give taste to the mixture), the mixture remains permitted even on Pesach, despite the fact that if the mixture occurred on Pesach itself, even trace quantities of chametz would make it forbidden.[13]
The most straightforward case of a physical mixture that avoids being forbidden due to the principle of chozer v’nei’or is bitul based on volume (when there is 60 times more non-chametz food than chametz). The form of bitul in an eino ben yomo chametzdik pot, which gives negative taste, is also one of a physical mixture, and its bitul status before Pesach is therefore similarly retained throughout Pesach itself.[14]
We need to use the idea of bitul based on volume to be lenient in your case for an additional reason. It is highly likely that small amounts of actual chametz got into the food, whether in the ingredients or from the pot’s surface, the work area, or storage containers. We can assume that these will be trace quantities of chametz, which were batel before Pesach based on a volume of 60 times more non-chametz in the food. As above, chozer v’nei’or will not apply to forbid the food in question.[15] Thus, food prepared normally and cooked before Pesach in a standard pot could actually be permitted to eat on Pesach. Nevertheless, our minhag is generally not to rely on these halachic leniencies, but rather to buy or prepare food that was in a chametz-free environment.
If one will not eat the food in question, may he at least keep it around? There is no violation of bal yeira’eh (possession of chametz) when there is only taste of chametz without any discernable piece of chametz that is not batel by 60.[16] While according to some authorities,[17] it is permitted to leave in one’s possession any food that is permitted to eat on the level of Torah law, the more accepted approach is to not leave most foods[18] that are forbidden to be eaten, even if the prohibition is only Rabbinic.[19] This does not apply, however, to a food one does not eat only due to a chumra. Even so, it is proper to remove such foods from the places where kosher-for-Pesach foods are kept (such as the same freezer), lest one mistakenly eat the wrong foods.[20]
If you put such food in a different place (e.g., a different freezer or a section of the freezer that is taped off), you are not required to sell it, but you do not lose anything by including it in your sale. Although you report that you do not sell certain types of chametz, stringencies regarding sale of chametz apply to cases in which you must rely on the sale, not when you choose to sell in order to facilitate a stringency.