It's not helpful that there is conflict between the FAA advisory on fuels for certain engines, the ExxonMobil World Jet Fuel specs brochure, and the P & W Canada, Service Bulletin.
No conflict at all really onetrack. The Exxon document confines itself to fuel refined purposely for aircraft use.
The FAA has given by its own authority operators of TPE331-1-101Z engines to use diesel. From what I can ascertain operation of this engine is confined to agricultural operators.
P & W approve the use of diesel subject to the limitations given as you note (temperature).
Also note NATO F-76 diesel may be used in certain helicopters.
"(ExxonMobil) does not support or approve the use of automotive gasoline or diesel fuel in piston engine powered aircraft".
This is merely the company giving its position for possible liability action. The FAA, and many other aviation authorities, have given approval for the use of automotive gasoline of approved quality in certain aircraft. I've not checked diesel powered aircraft as to whether diesel use is permitted against the usual jet fuel.