Thats a straightforward swap, I would pull the motor and box as a unit. Some early 1300's have an odd box with the box and bellhousing integral as one unit but I think the tailshafts / splines etc are all the same.
My money on the diff ratios is that you will find they are both 3.77:1 so leave that as is. A MK2 rear end will go straight in , just use the right bottom spring / shock mount plates. The only advantage to doing that is if its a genuine 2 litre rear end you will get the bigger 9 inch drum brakes.
I have run 2 litre Mk1 rally cars for about 10 years, both cars using the MK2 rear ends with early MK1 axles (see below) and am yet to break a U bolt, I don't know what the theory is on that one?
You will likely find that the axles in your original 1300 Mk1 are actually stronger than what is common in a MK2 2 litre rear end. The axles to have are the ones without the big boss on the outside of the hub, the MK1 axles actually have a little more material around the spline area (MK2 axles are machined down near the spline to try and remove the stress raiser that happens with the twisting motion, sound idea engineering wise but when they break, they usually break right at that point).
Cheers
Shaun B