Finally unit #3 passed all tests and I used it for about a week. Even the tape mechanism is now working great. I finally got a solution for the white lever and the play/fast forward problem. All I need is to create another video explaining what exactly I have done.
To ensure that the lever snaps back into its default position I created a small spring. It took a couple of tries to figure out which design can be used without any modifications like holes or the use of any glue.
First I tried some different designs with a simple wire and when I found the best method I used a spring from a biro which I bend the correct way. And finally, it is working absolutely great and the tape mechanism can be used at its full speed. This is something Philips should have done in the beginning to make the tape mechanism more reliable.
The only thing left for unit #3 is the integration of a Bluetooth module which I already have. Just need to find some time… in the meantime I can enjoy some music from the eighties…
