I don't doubt you've read the constitution, I wonder how familiar you are with history though. Just because procedures are laid out In a constitution, it doesn't preclude a constitutional crisis. 1800 there were procedures that laid out how to select the president and they were followed. Due to unforeseen circumstances, however, there was an opportunity for Aaron burr, or even John Adams to win in the house. If that had happened, despite the words of the constitution being quite clear on the procedure to follow there would have been civil war. Massachussetts and Virginia had already called up their militia (to march on each other) and if it wasn't for a representative from Delaware, who realized that the upcoming war would likely be fought in his state, the civil war would have come early. The constitution had clearly stated procedures, but because those procedures flew in the face of the spirit of the law, it percipitated a constitutional crisis that nearly lead to bloodshed.
Now what happens when Americans find out that with a viable third party presidential candidate, that in the likely event that there is not majority in the electoral college, the Republican Party wins every time. I could see two outcomes, the reemergence of a two party system through alliances and realignment (as routinely happens in American politics)or a breakdown/overhaul of the system through war, amendment constitutional convention etc. I hardly think that people would accept a second or third place party consistently winning with under 33 percent of the vote. Sure, the words may be written in the constitution, it doesn't mean that they will be accepted.
Regarding your statement about not viewing the election in a vacuum. Again, you should look at some history. In the late twentieth century third party presidential bids have not been accompanied by successful third party insurgencys down ticket. Perot won 20% of the vote, who associated with him sat in congress? No one. George wallace won 5 states and 12% of the vote, how many party members associated with him sat in congress, none. Sure, one day we might have a substantial third party, built from the ground up with several seats in congress. At that point we would probably see parliamentary style coalition politics to decide the executive. But even that would be problematic because out constitution is not built for executive power sharing, one person cpntrolls the branch for four years and he doesn't rely on party support. Whatever would come of that, we can safely say it is FAR off.
Point of the matter is this. You said you read the constitution, and since you did you know that the word party is not mentioned once. The constitution is not suited to parties. After 1800 it was amended so it could account for two parties. Since then the us has had good luck in that it has never had to deal with strong, persistent third parties and more than the occasional election in the house. I honestly don't think it can and why would it? It wasn't written with them in mind. Any successful third party without a reverting to a two party system, in my opinion, would lead to the rejection and overhaul of out governmental system