I have a couple of the cartridge adapters, one by Winchester and another by Marbles. The Marbles adapter body has four spring-fingers which grasp the cartridge when inserted in the front, such that the .32 ACP case is positioned where the chamber neck is. The rifle firing pin strikes a long plunger-type firing pin which sets off the cartridge.
The Winchester adapter is like a nickle-plated steel cartridge case and the cartridge is inserted from the rear, resulting in considerable free bullet travel before the bullet enters the rifling.
Group size with the Marble's adapter is in the order of an inch at 25 yards, the Winchester about twice that.
As for loading the light pistol bullets for gallery or small game loads in the .303 British case, I've had the best results using dead-soft bullets of nearly pure lead, as-cast and unsized at .314-.316" diameter, with the lightest powder charge which would reliably eject them from the barrel every time, about 3 grains of Bullseye, TiteGroup or Trail Boss is about right. If using heavier charges take notice of the report and keep velocity subsonic. Avoid loads which "crack~!" Supersonic loads are OK for varmints as long as they don't lead the barrel, but in the military 1 in 10" twist barrels I have found them less accurate than slower loads.
73 de KE4SKY In Home Mix We Trust From the Home of Ed's Red in "Almost Heaven" West Virginia