I have a Carvin Bolt 5 Fretless, which is the original version with a top load bridge only (current version has body thru option). It has a Hipshot bridge that once your B string goes past .125 or .126, it actually becomes too large for the bridge and you must either go to the tapered string route, contact core, or actually modify your string to fit (I can hear the gasps from readers now

).
I have used both the original Carvin tapered sets (.40-.128) and a set of Fender 8250-5M strings with a tapered E and B strings. I thought both sets were decent sounding, without the overtones you mentioned, but the sets were not too much to my liking for different reasons. I also thought, at the time, that non-tapered B strings sounded better, with a thicker sound. No scientific research to give you on that other than non-tapered strings also were the top pick in a string shootout Bass Player had at the time.
It could be just a quirk of the particular set on your bass. I have no experience with SIT's 5 string powerwound sets, but I have used the 4 string versions of the set without any noticible problems. I was thinking about trying out their 5 string Silencers.
You might want to give the Carvin or Fender set a whirl. Both sets are nickel. I am thinking about giving the Carvin set another try. Also, you may want to take the bass with the new B string and get a tech in your area you trust to see what the deal with the intonation is.
Best of luck with whatever you decide. I wish I could have been more help.
FG