Don't throw away the old unreadable tapes, I'm sure they can be read other ways.
Long ago I built an interface to the 1531 to allow tape duplication via my external Aiwa tape deck. I tapped the signal somewhere near the output of the device, sent it through some TTL gates to make its shape more squarish, then it went through a voltage divider into the deck input. Results were astonishing: I didn't have any tool at hand to condition the signal, but merely making it more loud and clean did wonders; no more hours spent adjusting the head azimuth. To be clear, a cassette which required adjustment could turn into a perfectly readable copy if recorded <i>without</i> adjusting the azimuth. In other words the problem wasn't the azimuth but low signal level (which is <i>also</i> a product of bad head alignment).<p>Now back to those old cassettes. If saving them from one device to another or sampling and filtering them doesn't work, it may just be the poor 1531 that cannot cope with a signal too much dirty because it lacks the brains to recognize it, but our eyes could indeed spot the problem. No kidding, In the old days I spent hours for every single music track cleaning them from vinyl scratches by zooming the waveform in Cool Edit Pro until I could see every single sample. Scratches became clearly visible for having a very different shape, often a few samples at a level not compatible with normal music. With time I learnt to spot them even more easily, and after finding them and verifying that they were actual scratches, I spent even hours for a single track cleaning them by reshaping the waveform, by hand, one sample at a time.
The reason behind this was Cool Edit's vinyl cleaning algorithm which at the time sounded like garbage.<p>Cleaning digital data should be much easier: one can load the waveform into an editor then zoom it until the signal becomes visible. It doesn't have to be readable by a 35 years old 1531, but merely recognizable by a human. Then either correct it manually (slow!), or write some macros to put x 1 or 0 samples where the mouse is according to a keypress. Then one can scroll the wave to a point where it starts an unknown bit; we know both data speed and carriers speed, therefore we know how many samples a bit is made of, this way when an unknown bit is met we know what to search for and based on this interpretation press a key which turns that series of unreadable samples into a nice 0 or 1 of the right duration and frequency. Still slow, but doable.<p>Analyzing the waveform at single sample level would also make possible to correct wow and flutter: again, we know the carriers frequencies and tape speed, so we know for sure how much long a bit must be and apply corrections where necessary.<p>Also, it might be interesting to sample all tracks at the same time into a multitrack file just like the cassette was a single side media. The reason being if the tape got damaged at a point, we can analyze the other track as well (yes, it's reversed but we're aware) to see if recovering one of them can help to save the other one too just by comparing a probably very similar damage done to two signals, one of which hopefully is easier to recover.