If the gearbox fits to the existing mounts and the gear lever pokes through the hole in the floor then get the prop shortened - much the easiest option. If the box doesn't fit the mount or hole, then moving the engine forward MAY work, but I don't know what clearances you have around the engine or the gap between front pulleys and radiator. As the mount and lever are probably at different distances apart on each box, you will probably still have to modify either mount or lever hole.
Looking at photos of the two boxes, the gear lever is at the end of the tailshaft, pushing it towards the rear of the car. If the car is still fitted with the original centre console this will be an issue. Cutting a hole in the tunnel is easy, making the console fit the new lever position isn't.
The position of the lever in relation to your left hand is worth considering. Sit in the car and hold the lever (removed from the box, obviously) 70mm back from the original position. If this is uncomfortable, then moving the whole assembly forward may be the better option, although a lot of work may be required.
Why are you considering using this box? The first 2 gear ratios in the Type 3 are longer so initial acceleration will be less. 3rd is almost identical and 4th is still 1:1