Got a picture of the offender?
This may be the problem - me not knowing exactly what you are speaking of, because having a union permanently affixed to a pump is zero issue and having two affixed to a pump is even less! And since you seem to think it is I bet we're thinking of different things.
Also on your Teflon tape. You should not use more than 3 wraps. Teflon is one of the few materials that cold flow. If you end up with a bunch of wraps sealing a leak, over time, you can end up with the Teflon getting out of the way,(cold flowing), and the leak returning. That's why Teflon is not used as a leak-stop. Its true roll is to allow later disassembly with minimum galling.
My old mechanical engineering boss used to rage at us for thinking anything we added to a threaded connection had something to do with sealing the connection. The threads themselves are designed to interfere and mate such that there is no viable path for the media to escape.
Also I hope you aren't unscrewing and replacing the tape over and over each time you go tighter... You should just tighten and watch for a few minutes. Still drip? Tighten further. Step and repeat until the leak stops. Continued disassembly and reassembly will result in galled threads and worse leaking.