I believe the 613 is the same headstock but with a lighter bed than the 612. If this is correct, then Mr. Oder is right: these machines are hydraulically activated. Even though you have a manual engage lever, hydraulic pressure is used to collaspe a bunch of friction disks together in the headstock to provide the link between the electric motor and the spindle. Pretty much the same principle of an automatic transmission. I haven't played much with the hydraulic manifolds in the back of our 612 but I think one was for the engage/disengage and the other was for the braking action. (The 62 has many more manifolds as it's completely hydraulically driven). If I remember to check while I'm at the shop this weekend, I'll finger through the 612 operators manual and see if I can come up with a few suggestions to your problem.
It might be that you're nothing more than low on hydraulic fluid and you start cavitating the hydraulic motor when you sling/slush a lot of fluid around the headstock. Or, your filter might be clogged. Or, your drain from the headstock to the resevior might be blocked... Lots of small possible easy-fix issues but I will double check on manifold adjustments for you.
Rex