Cable tension measurements, especially for low tension values such as the 20-pound range you are aiming for, are at best an approximation. If you adjust the tension at one ambient temperature, it will change at other temperatures due to the thermal expansion of the different materials being used (for instance, an aluminum airframe and steel or stainless steel control cables)--that's just the nature of the beast. There are also lots of other variables that affect it.

IMHO, investing a lot of energy in coming up with an electronic gizmo such as you describe, while it would be a fun exercise, would not gain you much. My suggestion (after building many EABs over the last 45 years) is to run your cables through the airframe, leaving one end loose on each cable; then hang a 20-pound weight on the end of each cable and get a subjective feel for the tension by deflecting the cable using your thumb and a couple of fingers. Then remove the weight and do the final adjustment until you get about that same subjective feel.

I just completed the restoration of a 1946 Cessna 140. The "official" rigging procedure (although in 1946 there wasn't much official information) says to adjust the cables to 30 pounds tension; however, everybody knows that if you do, the controls will have too much friction, so owners typically back off the tensions just enough to reduce the friction, using the technique I described to get a subjective feel for the resulting tension.

I suspect the airplane you are building is an ultralight-type (or maybe a slightly heavier EAB); experience has shown that the control cable tensions for such airplanes are typically not that critical, as long as you've taken the "slop" out of the cables and applied a little tension beyond that.

Hope this helps!