Solved

Here's the situation. I've got a low-end bike with balky rear shifting. The rear derailer is the cheapest of the cheap, a Shimano TZ-30 on a 14-28 7 cog freewheel; and it got banged and the pulleys were angled in towards the centerline. I gently straightened them as best I could and they look very close to proper alignment. I also replaced the god-awful cheap grip-shifts with old Suntour 7-speed indexed barcons and replaced the cable and housing at the same time.

The problem is that I cannot get the low gears (big cogs 7-6-5 / 28-24-21) to engage without autoshifting, skipping, etc. I've tried in both index mode and friction mode with the barcons and the problem is quite severe even with careful and slow shifts in friction mode. Since the freewheel and chain only have a couple of hundred miles and show no signs of wear related stretching, I doubt that is the issue.

Because this is effectively my first bike both as a rider and as a mechanic, and because I'm rather budget constrained, I'm trying to determine whether the problem lies with me, the shifter/derailer setup or the derailer itself. I've gone through various and sundry articles on sheldonbrown.com and other similar places and am stumped. I'd but a new derailer -- they are not expensive -- but if the rider or mechanic are at fault, replacing one working part with another seems silly.