Here is a partial view of a Diamond T transporter from the 3 Cdn Fd Pk Coy. From the movie footage showing Sherman IIs from 44 RTR moving through Thaon France on 20 Jun 44.
Note the crooked Allied Star.
According to the War Diary the transporters were called "DORA" "DOT" and "DAISEY".
Also from the War Diary 17 Jun 44 - "Unloading commenced at approx 1330 hrs and completed by 1700hrs, with difficulty with the Transporters." - "D-5 party was coming ashore. They came by LST and in beaching the vehs struck a mud hole so that most vehs had to be towed onto beach laterals. One trailer with two D'4s got stuck and became tidebound to a depth of seven feet for some time before recovery."
Here is slightly further on the film showing a D4 on a trailer. (what is the official designation for this trailer?)
And a still photo from the opposite direction.
Frank L. Dubervill/Canada. Dept. of National Defence/Library and Archives Canada/PA-133748
Caption: "Traffic jam of tanks and trucks moving in opposite directions."