The NXS 5.5-22x56 has low glare and fairly high contrast. I would be surprised if you found that a sun shade was needed for hunting. I would test it under setting sun conditions like you mentioned. With the sun shade off, vary the magnification from low to high and see if the contrast decreases as the magnification approaches the max. If so, repeat with the sunshade on to see if it makes a difference.
Regarding blue painter's tape, it is 0.005" thick and likely will not easily fit inside machined rings like those from NF. Also it isn't weather resistant and the tape material isn't very strong. If the ring shears the tape when the ring is tightened, the tape will likely tear and bunch up, creating a stress point. Plus the surface texture is rough, so the contact area may not be as high as with the machined ring surface.
I have a lot of experience using tapes of various kinds to line the rings. I've found a polymer tape that works well in some applications. It is 0.0025" thick, very strong and weather resistant. HighPowerOptics supplies it to customers for use with lapped rings and machined rings that do not fit tightly.
Be aware that use of machined rings does not guarantee that both rings will be coaxial. If the base is installed improperly, it could be bent or twisted and even machined rings will be out of alignment. Then you could have problems with the side focus, point of aim shift, ring marks, etc. If the base is not straight, fix that first by bedding the base.
In general, for machined rings I recommend checking the ring alignment. If the base is straight and the rings are coaxial, install the scope without anything between the ring and tube. When in doubt about the ring alignment, lap the rings even if they are machined. Tighten the ring screws using the proper screw torque. If you find that the scope slips due to recoil, then consider adding something between the ring and tube. Otherwise, you're GTG.
