IIRC the Coletti box was only used by the teams Moss drove for, as Cooper wouldn't allow Moss to use the ERSA gearbox (Presumably to try and make the Moss cars uncompetitive with the works cars). The design of the Coletti box was OK, it was machining errors which caused the unreliability.
I think the F3 Cooper's box had reverse, it's nearly 50 years since I last drove one. The FWD to RWD change was accomplished by just turning the diff over from left to right. Limited ratio changes were effected by splitting the box at the diff housing and changing transfer gears, which, of course, change all the ratios relative to the diff ratio - In effect one was really only changing top gear to achieve max revs on the longest straight. Sounds easy, it wasn't, the gearbox was probably heavier than the "A" Series engine, and single handed, took hours, whereas changing ratios in a Hewland Mk9 could be done in about 20 minutes.