From the new book on the Mille Miglia - from an interview of Goodacre by Julian Hunt 1981;
"In Dieppe I met Arino & Pino Gandalphi from Mr Nicholl's Rolls-Royce agency in Milan. They had driven from Italy in an unblown Ulster which I was to take back to Austin's London service department in Oxford street. So the Gondolphis took the race car through the Simplan Tunnel to Milan..."
Goodacre then gets the train to Italy and races the supercharged car.
It then says that according to Orsini and Zagari (The Scuderia Ferrari) the Scuderia had taken over a supercharged Austin Ulster which was probably the Goodacre / Trevisan car and entered it in the 1932 Mille Miglia. It was prepared by Nicholls, but although the crankshaft had exceeded its 40 hours racing life, it was not replaced and broke. As a result the car failed to start the race.
The painting it red bit could just be romantic legend...