This should be fun...
I was using ellipses (...) to indicate a sense of sarcasm and slight disbelief, and you may have me on an error of punctuation there, although I would argue that my use was, at least, rhetorically effective, and thus, legitimate. However, the use of ellipses has little or nothing to do with the status of a sentence as a run-on or proper sentence. The main question has to do with the use of the word and.
And is a conjunction proper, not a conjunctive adverb. Synonyms include along with, also, furthermore, including, moreover, and together with, as well as various forms and uses of the word addition. I chose not to use these synonyms or other varieties of conjunction or conjunctive adverb for a number of reasons, but three are paramount.
First, I felt that none of the afore-mentioned synonyms carried exactly the right meaning, proper or connotative, to convey what I wanted to convey. And was the only option I had to convey what I was after.
Second, none of those synonyms would have fit properly into the sentence - or at least, not as properly as and did. While there is some debate about the grammatical propriety of using such phrases to connect dependent clauses, I preferred and over the other options more for its connotative meaning than its grammatical status.
This leads to the third and most important reason, which is a question more of rhetoric than of grammar. There is a rhetorical figure constructed by the repeated proper use of conjunctions of addition in a sentence. This figure imparts emphasis and indicates disbelief and (depending on context and usage) sometimes sarcasm and/or mild contempt. (Sorry, I'd love to give you the fancy Latin name, but I can't remember it, and I'm not about to dig out my Rhetoric textbook to remind myself.) For example: He devoured two cheeseburgers and two extra large orders of fries and three salads and a baked potato and some chili and two desserts and three drinks! As opposed to: He devoured two cheeseburgers, two extra large orders of fries, three salads, a baked potato, some chili, two desserts, and three drinks! See the added emphasis and the building effect that conveys (in this case) disbelief? While it could be used ungrammatically, this figure, in my sentence, is a valid use of and because and is used to connect a series of dependent clauses.
This points to the most important reason why my repetitive use of and in that sentence did not make the sentence a run-on sentence. A run-on sentence has a very specific definition according to rules of English grammar. It is a sentence formed by a series of independent clauses, strung together using conjunctions. As you've pointed out, the conjunctions most commonly misused are and, and so, and and then. However, the mere presence of those conjunctions, even in a large number, in a sentence does not mean that the sentence is a run-on. For the sentence to be a run-on sentence, the clauses must be independent - that is, capable of standing on their own as complete sentences, with the function of a complete sentence. This is not the case in my sentence, as the clauses strung together are (as I mentioned earlier) dependent. They are prepositional and, more importantly, adjectival in nature, and so cannot stand as complete sentences.
Holy smoke... yeah, that came out longer than I intended.
I suppose I must have really needed a good English fix... 
