You are correct that a yeast strain is the most common cause of phenolic aromas in beer. The classic clovey, phenolic producing yeasts are those used for German-style hefeweizens. These yeasts convert ferrulic acid from malt into the unmistakable 4-vinyl guaiacol, which smells just like cloves. As it turns out, wheat malt contains more ferrulic acid than barley malt and if you actually wanted to try to produce more clove flavor using the same yeast strain, using more wheat malt is one way to do that. This is just the opposite of your goals.
Weizen yeast is not the only type to produce detectable concentrations of this compound. Many of the Belgian strains produce enough phenols to leave a not-so-subtle fingerprint in the finished beer and some British ale yeast produce barely enough to be detectable. The other types of yeast that are known for the production of phenols are wild yeast strains. In general, a wild strain is any strain growing in your fermenter other than the one intended. The phenolic aroma from wild strains is usually not the pleasant clove found in weizen beer but is more of a strong medicinal aroma similar to those wonderful phenol sprays like chloraseptic that dull the pain of a sore throat.
Medicinal aromas can also come from the reaction of chlorine with phenols produced during fermentation. The dreaded chlorophenol off flavor arises when chlorine, usually from bleach sanitizers or heavily chlorinated water, and fermenting beer commingle. One precaution to take if you suspect this to be the problem is to eliminate chlorine from coming into contact with beer. That can be done simply by making the decision to not use bleach as a sanitizer or being sure to rinse thoroughly after use. Also, be sure to use brewing water that is chlorine-free. One method used to remove chlorine from water is to add potassium metabisulfite (found in Campden tablets).
These days there are plenty of good brewing yeasts on the market and if you are pitching yeast from a well-known supplier, I doubt the yeast is contaminated with wild yeast. In the late 1980s and early 90s that was not uncommon, especially in some dried yeast, and phenolic aromas were often blamed on the yeast supplier. Today, if the phenolic aroma comes from the yeast it is probably a purposeful trait for the strain. So, switching strains may help alleviate your problem.