Michael,
Being curious, I just took a look at the on-line manual for the TS3612. I have a Jet cabinet saw but used to have a Delta CS so I thought they would be similar and could tell you all about the offset shaft Delta uses for that adjustment. They're not even close in design and it looks as those the backlash allowance is set by the parts (no's. 34-37) on the screw shaft. The manual isn't all that clear but I would suspect the two "O" rings as being the potential culprits or the retaining nut came off.
An experiment for you to try. Push in on the height adjustment wheel as you crank it up and down. Now do the same but pull out on the wheel as you adjust the height. Does it still clunk ? If it does, you may have a bad worm gear or a real bad build-up of resin on the gears causing them not to mesh correctly. A hardened deposit on the worm drive gear would cause the clunking. Been cutting a lot of borg pine lately ?
Bob S.