Not sure if this is your problem but I got my Thorens turntable
(similar design to the Linn) out after many years of storage. It also
played slow. However, after cleaning the belt, platter and spindle, and
oiling the bearing it then played at the correct speed. The start up
time was also about halved. The belt was old and stretched (still is)
and this type of design tries to use the minimum tension necessary to
do the job. It appears that all the accumulated gunge plus the stretch
was sufficient for the belt not to grip properly on the spindle at a
guess.