Is there a written rule somewhere that people cannot sell the same item via multiple accounts? Or is this something that is more along the lines of a mod's interpretation of the rules?
I don't think there is one that explicitly says You cannot use alts to sell the same thing so you can take it as my interpretation if you wish, but it directly contravenes the one thread per person and one bump every 24 hours rules. It can certainly be added to the rules, but this is exactly why BadBear was against posting them in the first place because people then just try to evade them on technicalities. OP knows you can only have one thread per person per same item/service. He knows you can only bump once per 24 hours, hence why he uses multiple accounts and dozens of others to bump them. It's a direct attempt to evade rules and spam the forum. He was told about this numerous times, on numerous accounts and had numerous bans yet he ignored them every single time and continues to do so.
If you are selling the same thing via multiple accounts *AND* are bumping each accounts' respective threads every day, then you are, at a minimum rubbing up against the one bump per 24 hours rule.
I guess my concern about mandating that you can only sell the same item via one account is that it gives incentives to not take unpopular stances on issues, which is anti-freedom of speech. Although selling the same item via 6 or 10 accounts is somewhat 'spammy'. However, if someone is selling the same thing via that many accounts, I think there is a decent chance they are breaking other rules anyway.
For clarification, I don't disagree with the OP's ban, assuming that what you say about him is true (or mostly true, if he is able to poke a small hole in what you say). Also, considering that he received warnings via PM from moderator(s), even if the rule violations he was warned about were not actually against the rules (I would not say this is the case), his appropriate course of action would have been to either reply to the PM to get the moderator to agree that no rule was broken (or escalate to a mod with a higher authority to get a higher authority to agree that no rule was broken), or he should have opened a thread in meta for discussion, with a resulting consensus among those that matter that no rule was broken.
I am very proud to only operate a single account. 
No you don't lol.