Advice needed on adjusting rear derailleur.

I'm trying to adjust the rear derailleur on my bike (Shimano Acer X in
the rear, Gripshift shifters in the front, 21 speeds). I've done
plenty of research on it, spent a few days on it, but all without
success. Problem I'm having is, I can't get it to shift perfectly in
both up and down (high/low) directions, on all 7 sprockets in the
rear, and all 3 cogs in the front. The trouble areas are usually the
middle gears (ie. 3rd or 4th sprocket from the smallest), or
upshifting from the smallest gear. When I fine tune it so that
upshifting is perfect, the downshifting develops problems; and vice
versa. I've tried making adjustments to EVERYTHING; the barrel
adjuster on the front grip shifter, the barrel adjuster on the rear
derailleur, the tension of the cable, the placement of the derailleur
before the cable is pinned down, the H/L adjustment screws, the
B-tension screw, the positioning of the guide pulley - everything.

There are even times when everything seemed perfect, shifting was
flawless in both directions, on all sprockets. But after cycling
through all sprockets a few times, shifting problems developed as
described above. This change in performance can only be due to the
action of tightening and releasing the tension on the cable, through
the act of switching gears on the gripshifter. But I've ensured the
cable was tightened down very securely, and the cable, like all the
other parts on the bike, appears to not be in a worn condition (the
bike has only seen maybe a year's use). Any suggestions on finding a
solution?