Terminology is very important .. just to make sure we are clear:
Double density is the standard used on the 5150, 5160, and the Jr. It gives you anywhere from 160 to 360K on a disk depending on the number of sides used and the formatting.
High Density is the standard used on later machines, like the AT when equipped with a high density drive. It gives you 1.2MB (5.25") or 1.44MB. Other variations are possible with formatting tricks.
Formatting and density are not closely related. Density sets an upper limit on formatting, but that's about it. For example, you can take a brand new 1.44MB drive with high density media and lay a 720K format down on it. How? Use only 9 sectors per track. That's the same format used by a double density 720K drive, but on different media.
Could you do the reverse? Not really. You can squeeze a little more out of a diskette with formatting tricks, but if you try to squeeze too much it doesn't work. A double density disk might survive a format in a high density drive (with a high density format), but expect to lose some data.
See
http://www.brutman.com/PCjr/diskette_handling.html for the gory details ...
Now back to the original problem .. If the drive was designed to be used on a n IBM compatible PC, then it's going to use soft sectored double density diskettes. Hard sectoring on a 5.25 would be quite the oddball, and it wasn't used on IBM compatibles.
I'd still look at cleaning and timing .. as Terry pointed out the timing marks are very visible, and the strobe of a flourescent lamp will show you the timing. (Good or bad ..)