Interesting dilemma you got there. I searched the web but then it would be unreasonable to think you hadn't. I found something called a memobelt which was supposedly the same or similar.
However in thinking about it, being a scribing machine of sorts, and given the time frame I would think two things, well one.....
It is unlikely that the unit used a capstan. Crushing the media would not be desirable.
As such that means the media speed would vary as it accumulates on the reel, which we really cannot call a takeup reel because of the lack of a capstan and pinch roller. I guess it would be called a drive reel then.
I don't imagine alot of problems with this, because some things can just be figured out. Now I have gone into wiki and as you probably know the JFK assassination is recorded on this medium. The article I read also states that there are references due to police calls which do denote the time one way or another, but that data are better used in fine tuning, it seems that you need more of a ballpark figure right now.
As such I would attempt to take a picture of a section of this belt media. In fact I would do it at the beginneing of a reel as well as at the end. Since the information is scribed, like a phonograph record groove, you should be able to figure out the speed by the length of the modulation in the "groove".
It is logical to assume that they used the minimum speed possible for intelligibility, therefore figuring the minimum bandwidth for speech what do we have ? I would think that 600 - 4,000 Hz would be enough. Looking at the groove should then give you an idea. The high frequency limit is the key,. And remember they didn't have high compliance Shibata stylii when this thing was invented. You may need quite a length of it, run it through something for film or whatever, and use magnification. Find the shortest "wavelength" undulations in the groove you can, and assume it's a couple of Khz. Then you can figure the IPS from there.
I wonder how you intend to pick this up really. Optically or with a stylus ? I mean would you somehow fit a magnetic phono cartridge to this whatchamacallit or let some type of LED and optical sensor array do it ?
This intrigues me just because it is different, and the fact that I am stil a Beta dood. I even have a one inch vodeotape hiding in the basement, still waiting for a machine that can play it. I used to own a Cartovision !, but I did buy it used.....
Data preservation and restoration is a real field of endevor, I mean people do devote their carreer to it. I myself would pay money to have what I have recorded on Beta for example in the old days. In fact I even worked on one of those Technicolor VCRs. Actually eight millimeter but not the Sony type that was standardized about a decade or so later......
Aaaa, the good old days.
J