Risking attack from all sides, I'll venture a semi-informed opinion.
I've owned a 'lower end' Speedster for almost eight years now. I use the term 'lower end' reluctantly (and without consulting counsel), but my older VS was built in haste and with more an eye towards price than Speedsters from some more up-market shops.
I have no experience with Chesils, but from reading reports here by owners who join us from time to time, my impression is that build quality is somewhat less than my VS. (Again, my general impression, and without advice from counsel.)
I've never driven a modern Morgan (if it can be said there is such a thing), but I have visited the Malvern works, taken the tour, and spent a few hours watching them being built.
So, with little hands on experience and making many assumptions, my feelings are that you should definitely hang on to the Morgan until you've driven a newer Chesil. I think the build quality of the Morgan - especially the finish - is likely to be higher than the Chesil. The suspension and handling of the Chesil are probably at least as 'Edwardian' as the Morgan. And the drivetrain of the Morgan is almost certainly stronger, smoother, more drivable, and much easier to maintain, with high quality OEM parts still readily available in the UK, and experienced service folks everywhere.
There seems to be an inexhaustible demand for new Morgans in the UK (last reports I saw were that the works can't keep up with it), while I'd doubt that's the case for Chesils.
It could be that Chesil build quality has improved since Westfield took over, but I'd want to drive a new one and talk to an owner or two before letting the Morgan go.
Good luck, and please keep us informed of how things work out for you.