I'd only use a full syn, and FWIW there's this list of approved oils that ZF publish and all the ones on the TE11b list that applies to the 4HP22E are....
Full synthetics!!
To be on that list it means the oil has to be submitted to ZF, your money paid (not an insubstantial amount) tested and then a license is issued if it passes their wear and performance tests.
And another FWIW, all the oils on the TE11a/b lists meet or exceed the old (as it's superseded) Dexron IIIH spec
The most respected, well regarded oil for these trans is Castrol Transmax Z, a full synthetic fluid (PAO/ester)

