Nice deck, I love them. You shouldn't need to time records, the markings on the platter are a strobe.
The little black knurled knob inside the speed changing knob is the fine tuning for the speed - sounds like this needs adjusting. (Later Beograms suffer from slowness because the bearing grease dries out, but the 1000 seems less prone to this, either because the bearings were better or because the grease is so old it has hardened and worn smooth again???)
The bad news is that the rod that links the black knob to the motor tends to seize inside its sleeve - attempting to force it free will break the socket inside the knob. The speed changing knob simply pulls off, so best to remove it and see if the fine tuner will actually turn using a pair of pliers; if it doesn't then a few drops of penetrating oil left to soak in for a couple of days is needed before you take the motor out, and strip down and clean the speed changing assembly properly.
Cheers, Steve