Chevvron
I think you could fit the Barge on the trolley but the wing ropes were too long. We overcame it by wrapping them around the struts once and then hooking the carabiner into the rings at the top of the struts as normal.
1 person stayed in the cockpit when being 'trolleyed' back to the Launch Point.
The main issue was that the Barge had a wider skid which meant it could be a tight fit (sticky) on the trolley ramp. Also the wing on the Barge was higher lift section and wider span so the chances of getting 'airborne' on the tow back was much higher than the Mk3 which we used tow at at least 25 mph (in the rush to get back to the launch point). I seem to remember that the tow speed for the Barge was not more than 15 mph on the trolley and maybe even 10 mph (memory fade)
The Barge was never really used for circuit training except for tall cadets who could not fit in the Mk3, staff training and mainly AEG (which entailed spot landing) so the trolley fit was not a major issue.
The Barge always seemed a hot ship to me compared to the Mk3 and the Swallow seemed like a spaceship compared to the Barge !!
Hope this helps and addresses some of the Trolley logic !!
Arc
Note: Being 'trolleyed' has a totally different connotation to my teenage sons than it did for me............