You have already selected your answer, but I would like to put a few more lines.

First of all, objecting to Marcus, I think that your first assumption is correct! We can store one hour of almost CD quality (14-16-bits, 44100Hz, stereo) analog audio into these commercial music casettes; i.e magnetic reels. So on a very rough basis you have almost a 600 MB (Mega Bytes) of data capacity there?? 

Of course, magnetic mediums have different uses, types and qualities.
And I think, one thing to mention at the beginning is that, the commercial casette have a tendency of losing its *quality*. This is especially true with music recording, where high-fidelity is lost after a few playbacks. Such an untrustable charcateristic makes them a bad choice for reliable data storage at high rates. Hence possibly lowering their available capacity, in
exchange of increased reliability and durability.
   
But the oppsite is also true: for example, IBM has developed the hard disc drive technology (very high density digital storage) based on magnetic recording too. Their circular shaped magnetic plates make it possible for random access with the help of a moving read-write head mechanism. Packing together a dozen of such magnetic disks and very sensitively controlling the head mechanism in between the plates, provided one of the most important and successful inventions of the computer industry. Even today HDD dominates, and SSD is still expensive, or Cloud is very unconvenient.

You have to be careful about the medium's physical characteristics, and which way you want to store data. The commercial audio casette system (magnetic tape, and read-write circuitry together) had a **bandwidth** $B$ of about 20 kHz. And I guess its SNR is about 60 dB. This can be an under or over estimation, if you consider what I've said at the beginning; CD-quality audio. Now to be honest, Casettes do not provide CD-quality (low-noise metalic casettes with Dolby type-s noise reduction is said to achieve a CD quality though), as there is some characteristic high frequency **hiss** noise in those commercial casettes, especially on the lower quality tapes. Therefore I will take 60 dB as an average estimate. Also note that this SNR depends on the frequency, as the noise increase by frequency, but I will ignore it too.

The (Shannon) capacity $C$ (in bits per second) of the medium is therefore:
$$ 60 = SNR_{dB} = 10 \text{log}_{10}( snr ) \implies snr = 10^6 $$ 
$$ C = B \times \text{log}_2( snr +1) = 20 k \times 19.9 \approx 400 ~ kbps $$


And assuming a two channel stereo recording this yields about $800 ~kbps$ channel capacity. Indeed, considering that CD had a much better SNR about 96dB, it has a channel capcity of $1.411$ Mbps. Then the commercial audio casette had an equivalent data rate about half of the CD medium. In one hour this makes about $360$ MB (Mega Bytes) of data.

The capcity is there, but how can you utilize it? 

The audio CD, for example, uses a very small tiny pattern on the circular track lines. The bits are placed as very short and very thin reflective vs nonrelective sections along the track lines that spiral from the innermost circle to the outermost, just like in Vinyl. There is no noise, but distortion due optical reflection, diffraction, and refraction, mechanical disturbances, which limits the resolution at which you can place or read those tiny dots on the circular tracks. 

But magnetic medium is totally different. You store an electric signal (a magnetic one) into it. And you have noise. But you have an advantage over the CD. The CD medium has only one amplitude level indicated by a reflection or no reflection. This is due to the specific mechanism used to write and read the bits. But the magnetic medium can provide multiple bits per symbol to be written, as multiple amplitude levels can (in principle) be supported. 

This kind of M-ary encoding is very well utilized in Satellite communication, where 256-QAM is used to take advantage of (relativlely) low noise transmission channel...  

Coming to your Kansas City Standards, it's not about the magnetic medium capacity, but about the commercial phone line *allowed* channel capacity which was quite limited to about $3600$ Hz back then...

So the conclusion is; if you can afford a suitable encoding technique, in principle, you can store about 360 MB of data into a standard commercial magnettice type cassette. There are low noise (high SNR) casette types (such as Cr or Metal) available which would increase the capacity. Or at least you can roll a longer reel to increase it. Whether you can accomplish this or not is another practical concern though.