Ed,
In answer to the points you raised...
First off, the Sulphated Ash test is a really old test. It harks back to a time when there was a EXCESS of sulphur in fuel and oil. I have a vague recollection that SA was originally limited to 1.5% max because of spark plug 'whiskering' (I might be wrong on this because I heard this story when I was still working in Fuels).
TBH, when I first started out formulating oils, no-one paid much attention to SA other than as a tick-box exercise. There were lots of tests where oil related deposits needed to be considered but none related directly to ash. Gasoline sludge, piston ring/groove deposits and Teost deposits all figured prominently. Interestingly, combustion chamber deposits (which I think is what this thread might be focussed on) do not, as far as I know, figure in any engine oil specification.
Regarding the issue of whether there is enough 'bonded' sulphur in Detergent & ZDDP to ensure that ash is naturally 'sulphated' (even when both the base oil and gasoline are essentially sulphur-free), I am not sure this as clear cut as you suggest.
For starters, the great bulk of Calcium in overbased Calcium Sulphonate exists as Calcium Carbonate; not Calcium Sulphate. There is a bit of so-called 'neutral' Calcium Alkyl Sulphonate present but this is primarily there to ensure the Calcium Carbonate is kept in colloidal suspension. You should also bear in mind that some Detergents (Salicylates and Calixerates) are entirely sulphur-free.
Ash from burnt ZDDP could be sulphated but could just as easily exist as Zinc Sulphide or even Zinc Oxide (remember that ZnO is what's used to make ZDDP in the first place so at high temperatures, it might just 'revert').
To be clear, I'm not saying you're wrong. I'm saying that in the olden days, when you had a massive excess of sulphur swirling around the combustion chambers, it was easy to think of ash being in the Sulphated form. Take away that excess sulphur, and things become less certain. TBH, I suspect no-one probably knows the answer as all of the analysis will be of ash laid down in the DPF itself, which of course could very likely change the chemical nature of said ash.