I do stuff like this quite often and have retained a Yamaha cassette tape deck as part of my rig for just such jobs. Actually, it's a dual transport tape-to-tape recorder which is significant, as we will see.
I set up a project folder on my DAW (Digital Audio Workstation - a fancy name for an ordinary desktop computer that's set up for recording) and using an old version of Steinberg Wavelab, started to record the analogue tracks. Side one, first tape. Sounds very odd in the monitors. A low frequency, grinding rhythm track. Aha, I thought, turned the tape over and had my suspicions confirmed: a deep, bassy set of backward vocals. Literally backwards. Like a song being unsung.
I realised that these tapes were the multi-track originals from a four-track recording device popularised by the likes of Teac and Fostex in the 80's - before digital recording was an affordable proposition for us mere mortals. Although they used a standard cassette tape, their format was (usually) to run the tape at twice the normal speed for better fidelity and use both stereo tracks in the same direction, giving four individual tracks. This enabled the layered recording of 4 individual instruments or vocals. With judicious planning, you could even record 3 tracks and mix them down to the 4th track and record three more! It was a clever, if inelegant use of a less-than-ideal medium and offered the creative musician the ability to explore arrangements and make demo tapes, albeit a low-fi and often frustrating affair.
I quickly ascertained that the source machine had long since been put out of its misery, rendering these tapes rather useless. Unless...
I mentioned that my cassette deck was a tape-to-tape machine. It offered something called "high speed dubbing" - essentially recording one tape to another at twice the speed, to halve the time it took. Although I hadn't used this facility in several decades, I remembered that you could monitor the Chipmunk-sounding audio as it dubbed. I hatched a plan.
I dug out a surplus C90 cassette as a dummy to record to: not to use, just to allow the high-speed dubbing feature to work. Sure enough, the A-side audio now sounded "normal". I recorded this stereo (or more correctly, 2 track) output to Wavelab on my computer. When this was done, I turned the tape over and recorded tracks 3 and 4 - which, of course, were backwards.
One of the hitherto fairly useless tools in Wavelab is the ability to reverse audio. This I did to tracks 3 and 4 and, voila! I now had four tracks of audio, prettymuch as they would've sounded on the original machine. (In fact it wasn't quite that simple; they sounded all compressed and "woozy", then I remembered these machines often used a filtering process known as Dolby C to help with tape noise and deteriorating trebles. Fortunately my deck has Dolby C. I switched it on and did it all again and the wooziness was fixed.)
I was amazed at how complex the original recording was: beds of percussion and synthesizer, guitars and vocals with cathedral-like reverbs. Remixing this was going to be rudimentary at best; instruments that were "bounced" to the same track could not be separated and aggressive effects could not be ameliorated. (Actually, there are tools that can do this sort of thing now, but it's way outside of my domain.) I chopped up the audio into separate songs and split the stereo pairs into individual tracks, normalised them (made them the same volume), added some equalisation and noise reduction (to reduce the inevitable tape hiss), repaired one or two glitches then saved all the files.
Next I pulled the files into my multitrack software (I use Reaper. You should too.) and aligned the four tracks with each other for each song. I spent the next few days mixing all the tracks down and while I was quite chuffed with the fact that I'd achieved a modest result with the help of a few unorthodox kludges, it was nothing compared to how stunned the recipient was when he heard his long-abandoned endeavours of 20 years before in full digital glory!
Dedicated to Andrew and Anna.