How can I convert this cast-iron cleanout to a proper air-gapped drain?
I agree with Ecnerwal, definitely use the threads for a much better solution. Don't worry about the iron's threads AT ALL, they'll cut and correct the wimpy PVC's threads as needed.
As a side note, concerning the VERY WRONG information out there about Air Gaps...usually from Home Inspectors. Air Gaps have absolutely nothing to do with sealing out smell, gases nor anything else. Air Gaps are nothing but a terrible back-flow prevention device.
Since this is a drain, you'll need to handle it, mostly (see below's opinion), like a sink drain, or more specifically, a laundry washer's standpipe to get it legal most anywhere.
You'd have a bottom shorter vertical straight pipe that leads up to a P-trap and another longer length vertical straight pipe (longer so volume can force out a clog) that goes up 30-inches, if possible, that you stick in or strap/wire-tie your hoses into.
I don't feel the vent and AAV in the image below are needed for your situation, as the open top of the Standpipe would be plenty of vent for your low-volume situation to flow properly. BUT, regulations may indeed require it, even though the pipe you're draining into is twice the size and doing the venting of anything nasty (technically, a wet vent)...you just need good flow.