I second the KAB...but I don't think your issue is speed. Speed will change the pitch but that would be uniform throughout the record. If the record is "slipping", as in the drag of the needle is pulling the record at times, then a fluctuation in pitch will occur. My guess is that your record clamp needs to be tighter or the cartridge is tracking with too much force (most likely the 1st issue).
Spindle hole being off center would contribute...I agree with above...look at record for warp as well. Speed is very important for constant pitch...but not fluctuating pitches.
Spindle hole being off center would contribute...I agree with above...look at record for warp as well. Speed is very important for constant pitch...but not fluctuating pitches.