Hello Tim
Speed change could be done operating on the two pushbutton (33-45) OR by a reed relay placed on the lower side of the turntable (The dark side of the TT )
To check this reed relay you have to open the unit (The Beo), and control the contact; could be some mech problem or there could be a cap defective, so you have to change it.
It is not so difficult but is better to let a technician check inside, if you are enough skilled to open the unit let me know (I don't know if skilled is the right word so read as " if you normally open a Beocenter 7700 once a week") :)
Let us know,
ciao ciao