How do you adjust the tape speed w/o splitting the box? Is this possible?

You need to get inside and do an adjustment
using a calibrated test tape.

I do my own adjustments by playing a song that I know, and making it play at the correct speed, and so it sounds 'right'.

splitting the box?

Well if you can use a long thin
screwdriver to reach the adjustment on
the motor than you dont need to open
the box.