Weird Overtones With Tapered B -- Fixable?

I just changed the strings on my Stingray 5 from La Bella Deep Talkin' rounds to Chromes flats. The La Bella's had a tapered B, and when I raised the bridge saddle to compensate, I got weird overtones on the fretted notes. I used to just ignore it, but then I noticed the same thing happened with the Chromes before I lowered the saddle back down. What else besides the saddle height is causing the issue, and what would it take to fix it? I'd like to be able to use another set of La Bella's without issue if possible since my band plays everything a half-step down.