I'm pretty sure those diffs are 1:1,they use the chain sprockets from the transmission to the diff case for the gear reduction..(something like a 10 tooth sprocket on the transmission and 60 to 72 teeth on the axle sprocket..)
If I turn one shaft a full revolution the other turns a full revolution too,only in the opposite direction..
I used one once on a home made buggy,after I got the steering box I had hooked up,it would turn the wheels the wrong way! (Had to turn the wheel to the left to take a right and vice versa!)--a slight goof in the engineering dept!.....so I put the diff in line with the steering colum..
The back side idler idea will work too,it just takes up more space,and now you have another chain that may fail,and more sprockets to deal with..if you could score two straight cut gears,they would turn in opposite directions ,and be less bulky and no chain to worry about..(I have used old iron camshaft gears for that purpose before,ones off junk push mower motors or chevy engines)..