The "jammed with rust" is probably contributing to your difficulties.
There is minimal clearance between the scroll and the two parts of the chuck body and between the two body parts themselves.
Any corrosion in this small space will make separation challenging.
Submerge the chuck in a bucket of diesel for a week. Remove it and go around it with a wood mallet or nylon hammer. You can buy an attachment for an SDS drill to rattle the sludge from domestic radiators. Applying (a home-built) one of those will also assist. You need lots of gentle, sustained vibration, not heavy blows.
Possibly better than diesel would be Evaporust or one of the unbranded products that do the same job, e.g
https://www.ebay.co.uk/itm/374293981667
https://www.ebay.co.uk/itm/115253455158
(Do compare the text, and especially the supplier's address, on the two items above).
The hassle is that the rust removal products require a clean item as they do not cut through rust covered in oil or grease, so you might have to degrease, hot detergent wash and water rinse before dropping into the solution.