The verb, 'to supe', has been around since the early 19th century, but only in the meaning of acting as a supernumerary player in the theatre, so it, too, is just an abbreviation. As you say, I have never seen souped, as in 'souped up', spelt without an 'o', Fred.
However, a century ago, one of the slang meanings of the noun, soup, was anything injected into a horse with a view to boosting its speed...a process rather similar to supercharging an engine. In a sense, therefore, there may not be that much difference between souped and suped!