Some stepper based drives have very basic tracking information, such as the CMI 6000 and 7000 series drives which use an optically encoded servo in addition to tracking bursts written between tracks onto the platters in the factory, which with a discriminator help position the drive's heads. See "COMPUTER MEMORIES CM6000 THEORY OF OPERATION" starting at page 9 available here.
Cylinder -1 is typically an engineering or control location on many ESDI and IDE drives. Steps beyond track 0 cause the heads to hit their end stop, at least in the KC-20B.
Judging by the rest of the diagnosis I am willing to bet that the band was stretched or fatigued before it was even disassembled. I can dig through my collection a bit to find one, but I do not think I have any spare KC-20Bs at the moment. What is the length of the band? I may have a bagged Kalok part somewhere. If not, the band is typically just a stripe of spring steel and is not hard to replicate manually. If you have a drive of particular value, I've found many machine shops can and will make them happily, as well as resurface crashed platters. Though they are still unwilling to coat them for me...
By "servo" I'm simply inferring a special track with easy-to-recognize data patterns. Need not (and probably not required) to be FM or MFM. The data could simply be recorded as signals with varying offsets from the track centerline, to allow the positioner to find the "sweet spot"
See my previous post linking to CMI's technical document on the inner workings of the 6000 series, which did exactly this. There are pseudo-tracks between every data track which contain a repeated high frequency burst which is separated to the microcontroller for basic positioning information. It sets outer limits of the track - The idea was that the head was imprecise enough in general operation to "hear" this high amplitude noise even while reading or writing other data. The noise alternates between even and odd track limits, which means that the perceived "noise" in reading should be exactly even at all times to know that you're in the middle of a track. Of course in practice this requires a lot of very fine analog adjustment and is often pretty inconvenient without specialized equipment, but the theory holds water. Kalok's Octagon II drives did this as well.
I would hesitate to even call them particularly fast in some cases. The maximum access time of an ST-506 with it's 3ms step rate is 500ms before settle time - The original 400K floppy drive in the Macintosh 128K has a maximum access time of about 430ms including settle time. Maybe it rotates faster but it was no faster in seeking than many floppy drives - And there were quad density drives available which had transfer rate over the ST-506 as well. There are some drives out there which are even slower than an ST-506, even with buffered seek. I can think of a few Epson and Microscience drives just off the top of my head.
There were floppy drives with a rotational speed of 3600 RPM? I've never heard of any. There were some 600 RPM drives; the original 3.5" Sony ones were like that, as were the 5.25" Drivetec units. I suppose, for the sake of argument, you could include Bernoulli drives (3000 RPM), but those really were a non-contact drive; really sui generis.
See "maybe it rotates faster"
With a 10K track size you will be moving the heads a lot. The expectation with a hard disk drive is that you are storing many files or very large files, and with FAT you will be seeking to the table often for small files and you will need to reposition the heads many times for large files. In my experience it's marginally quicker in day-to-day access than a high density 3.5" diskette drive.
I have no direct experience, although I own a 1325 and a 1333 which suffer from this issue. I have been told that there is a way to insert a shim in a manner which will permanently fix the unit, but I have not yet gotten around to bothering with mine. They are ugly drives and being counterbalanced rotary voice coil makes them rather bland in my opinion. The 1333 set itself ablaze for a short period - At that point I stuck them both back on the shelf and have rarely looked their direction since. It seems there is an official fanpage on YouTube which may have some advice, though. Might be worth a try there.
. A bit messy and a touch shocking. but it works!