Perhaps the word high is an abbreviation for the phrase "stinks to high heavens."
The metaphorical "high" reminds me of the equally metaphorical humming, as in the saying "[The smell was so bad that] it was humming." Yeah, I can appreciate the switch from the sense of smell to the sense of hearing. A smell so bad than it can be heard--now that's got to be bad!
To switch the metaphor, I can recall some smells that were so bad that they "hurt" (enter: the sense of touch)!
Can you think of something that smells so bad you can almost taste it (again, one of the five senses)?
How about a stench so bad you can almost see it? A "stink to high heavens" implies that its height can be seen and therefore measured (e.g., "It's a mile high.)
What about an odor so unpleasant you could almost cut it (the senses of smelling, seeing, and feeling?)
I'm sure you get my long-winded point.