Converting to MP3/ upgrading my original tape player?

You could as an alternative go for a HU which has retro touches about it. IME it is the source (HU itself) that aids the sound as much as the speakers, installation and amplifiers do (I have even been stunned at the difference in SQ with going from a factory CD to a half decent aftermarket item). Going from a Panasonic HU a little newer than yours in the Pug to simply a more modern item (initally it was a JVC AVX2, and then the trusty Becker), gave me more volume (I could actually hear the radio at speed, better sound quality and a stronger radio signal in the case of the Becker.) That was simply with radio playback to level the playing field.

I reckon a conversion to your HU can be done, but it will not be easy by any means. As for the companies have you considered going to the company who do the 5 button items? (If it is who I think it is, a number of half decent HU should do the job better .

For the above you could do what I did in my Porsche and Pug, which is to install a Becker, it looks a little more classic


As always there is another way....

If you have a smartphone which has Bluetooth, and your car has ISO connectors on the rear (you can always add these on) you could get a handsfree kit for less than £100 (the basic one in my Mondeo was £70), and pair your phone with that. I am quite surprised of the quality of the amplifier in the Bury Handsfree kit in the 1.8 Mondeo. In my case, the buttons are discrete and the tracks are controlled via the phone. You also gain a method of talking handsfree in addition to something which will give you voice guidance through the speakers if using a sat-nav on your phone .

Of course that comes with catches including non adjustment of fader or balance controls (but it does play in a stereo format) in addition to adding more gubbins behind the dashboard. If you are nearby and for whatever reason wish to consider this option I am happy to demo the car with you .

Ditch the panasonic and fit a blaupunkt instead. Back in the 80s/early 90s the golfs could be spec'd with a variety of decks from different manufacturers. High end blaupunkts were good bits of kit, powerful, had line in and outs and tbh look far nicer than panasonics offerings.
You could add a line in and even a line out to your panasonic without too much trouble if you have a good understanding of electronics. You could probably fit a more powerful amp too. The amps on most stereos from the early 80s onwards use opamp chips for the amp section, so you need to find what pin out your std chip amp uses, then find a more powerful version with the same pin out.
The line in needs to be connected to the volume pot if the radio has one and if not you need to work out the audio part of the radio circuit, find somewhere suitable to connect to, then find a way to mute the radio if it doesn't auto mute in the presence of an aux signal.
The line out is pretty simple. Find the inputs for the amp chip and attach some rca leads to the input, so you effectively bypass the on-board amp. Only issue I found was that the input signal was pretty weak. This could be sorted by making a basic pre-amp (it might even be possible to re-use and mod the pre-amp that will be fitted to the tape deck, something I had planned to try but never got round to doing)
I did offer a service to carry out such mods, but the vast majority of people appeared to want the work doing for peanuts, so I stopped doing them. Happy to give pointers though.
Personally if I were to carry out such mods for my own car I would start with a better period radio as those old panasonics are a bit naff compared to the competition. I am pretty sure some sony decks with cd changer control and rca out could be spec'd on later mk2 golfs (back when sony made fairly good stereos that weren't lit up like an xmas tree.)
Wouldn't bother with a modulator as that will degrade sound Q to below that of mp3 or cd.

From the hidden amps I guess you would adjust it from the MP3 player itself .