...it does screw in and out, just doesn't tighten.
I'm having a hard time visualizing that. If the screw moves in and out, it moves the body of the strainer in and out. How can it not tighten?
When someone describes a Zoomatic not tightening, my first suspicion is a stripped shell nut. The shell nut is the part that the adjustment knob shaft screws into. If it's stripped, there will be some slippage and the Zoomatic can seem like you can keep turning and turning the knob without it getting tight.
To see a shell nut (and possibly order one if need be), you can go to jp2creations.com, click on Parts in the left column, and select the Slingerland Zoomatic strainer on the right.
Another possible problem is separation of the pressure-fitted washer from the shaft. But if you've already looked into the spring fix, you've probably checked that.
Also, the knob is missing from the screw. Can anyone give any help or advice?
Jim Petty sells replacement knobs through the same jp2creations.com web site I mentioned above and he'll press the knob onto the shaft for you. The site doesn't have a price listed, but I'd guess it's more than a few bucks.
If you've got problems with the shaft and/or shell nut and you're missing a knob, the most cost-effective answer might be to find a replacement Zoomatic or at least a parts donor.