Oh, this is a nice one...
First off, you will ALWAYS have harmonics/overtones going on. The key is to have a head in tune with itself so you don't have a massive amount of dissonant overtones. That way, the overtones are there but won't disturb your ears and interact with other heads in an unpleasant way.
This has nothing to do with head stretching or anything like that. Assuming you have good bearing edges, a round tom, a round rim and a good shaped head, it's all about the tuning and head selection.
I had that head on a 16" tom for practicing (a friend sold me the Stage Custom tom and gave me the head) and it sounds kinda dull for what you're trying to achieve. Go for clear Emperors or G2s. Or Ambassadors if you're too much into Simon Phillips
Then it's all about the tuning process. What I do is finger tight, then the push the center-wrinkles out thing, and from there I start tuning the head with itself. The key element is that from 14" drums up it's on a range where many people have a hard time hearing tonal differences. This is what having a fine ear actually is, being able to tell a very close tonal difference and how wide your effective range for that is. My advice: for starters, tune it up to where you can hear notes next to the lugs more easily, have all lugs in tune with each other and then go back down in quarter turns until you reach the fundamental you want. You might lose a little accuracy while tuning down, but it shouldn't be anything of importance.
Both heads at the same tone is the ideal, but be careful not to have your bottom head too tight, as it will shorten the decay, or too loose, as it won't resonate enough. And you need that resonance to keep the sound going. A half step higher than your batter head is still ok. Same concept applies to your batter heads, of course.