No mate, Land Rovers right up to the end of original Defender have a transmission Hand brake on the back of the transfer box, and therefore acts on the prop shaft. Works fine as long as both rear wheels are on the ground or with series if it is...
When you get the broken shaft out just do not bother with a replacement until you find another axle or decide to fix the diff you have. At least it will not scrub on the corners, after all that is how it has been working for some time.
I would...
Been blead of late so that is good. Try the release the pipe thing and if pedal goes down good.
Next is to remove gear tunnel and have a look at what is going on with the slave cylinder. when you get that far come back.
TV's Mythbusters proved it is possible to polish a turd, but a turd is still a turd even if there is a shine on the outside.
Checking and sorting any issues with chassis, bulkhead and running gear is what should come first.
You may think that your engine is running rich but white deposits are the result of running lean.
If it were running rich they would have black deposits on the plugs.
A nice light brown is what there should be on the electrodes.
A Gunson...
That looks a great start to an interesting build, you should consider putting it on the members projects section
http://smithies.co.nz/land_rover/
Hopefully find what you need here