Oversize screw down crown issue/advice requested

Good afternoon, I have an oversize screw down crown on an Aquastar Atoll that I am having engagement issues with. An original crown is unavailable but I am wondering if the one I have may be helped with cleaning and gentle coaxing?

The crown screws onto the stem and onto the case tube without issue. It is when you use the crown to set the date, or adjust the hands that the "slipping" occurs.

Removed from the movement/case, this can be replicated by immobilizing the stem and turning the crown. It seems the inner crown tube is not engaging the outer crown tube.

There is a spring in the crown which allows the inner tube to move into and out of the outer tube a short distance. I'm sure there is a mechanism which should engage the two tubes together when the crown is unscrewed from the case, but I can't find anything on how this works. The spring seems to be intact and strong.

Should I attempt an ultrasonic cleaning and possibly a drop of oil? Any other advice?

Thanks for any help!

Thanks Archer, that makes sense. Would there be a way to immobilize it? Epoxy or superglue? I hate to think of it, but the crown is unobtainable and I would prefer it over a generic replacement even if it no longer screws down.