I'm HIGHLY suspicious of substituing aspirin for metasulfate (the active compound in Campden tablets). Different chemicals and I've never heard of aspirin being effective against yeasts at normal concentrations. Certainly not a single tablet or two (or more). Aspirin is not an effective antimicrobial in the concentrations that you would want to drink. It appears that you would need a concentration of 400 micrograms per milliliter to see an effect and that translates to 3.5 lbs of pure aspirin in a 5 gal batch (see http://gut.bmj.com/content/52/4/490).
You could burn sulfur and bubble the gas through your solution, but this really wouldn't be very effect and it really stinks.
The easiest way to remove the potentially problematic yeasts is to pasteurize. This is accomplished by bringing your solution to 145F for at least 30 minutes (or 165F for 1 minute, AKA HTST pasteurization - see http://www.dairyeng.com/applejuice.asp). This is what was done historically to kill bacteria and yeast. People who are potentially allergic to sulfites use this method instead of metasulfate. And I do this when I don't have Campden handy. Cheers.