I have removed and rewraped about 10 times with the thread. I washed all the fittings with a beer glass detergent to remove any oils. The threads appear to be fine (no obvious burrs). I used a wrench to tighten the valve down.
Not sure what else to try.
Looking at your picture, the tape looks kinda "thick."
Not all teflon tape is the same. Maybe you got a bad one. Some tape (from China, IIRC) is very thick and seals like crap. You want the thin stuff. Try to obtain some from a different source, if yours is suspect. Although not my preferential store, I'm using Home Depot's and that works fine. Get the big rolls, 540" per roll, you'll use them.
To clean the threads I use a brass (not steel) brush, and brush "leftwise," counterclockwise to remove old remnants. Acetone (nail polish remover, if in a pinch) is best for degreasing.
5-6 turns of teflon tape, wound tightly in the same direction as you would screw a fitting on, usually seals fine. The threads are tapered, so the more you screw it on, the tighter it gets.* I think you need to screw the fittings five or six turns together, on average, to seal tapered threads. The tape is a lubricant and a sealer at the same time. Using too much tape, does not provide a better seal as you can't screw enough threads on. Using not enough, the threads may bind which causes big problems later (galling), apart from leaks. So you need to find the golden mean.
* I'm not sure if the pump head threads are tapered (NPT), they maybe straight (NPS). The camlock and valve ends are definitely tapered.
You could try to screw the fittings together
just by hand, without tape, and check if there is excessive play. If there is, that may be a cause of leaks.
I would not use liquid pipe dope if you can prevent it. First, it's messy. And you got to be careful how you apply it. Some of it could squeeze out on the inside of the fitting which will get in your wort. Tape should be all you need. That said, In my previous home I've repaired the old boiler/heating system and tape PLUS pipe dope creates a better seal than either of them alone. Plus it was way easier to screw 2" pipes together. The liquid really lubricates the threads well. The new dope is supposed to stay pliable forever, unlike the old fashioned kind.
Last but not least, be careful when putting force on that pump head. You don't want to break it or snap the stubs off.
Hope this helps.