Working with defenders ain't going to go cheap, if you want a professional job expect between 0.7-1.0 mil with specialist sub-oem gear.
Variables are the YOM of the vehicle, and condition engine type, bulkhead etc and how well you intend to do it. My opinion is to stick to Land Rover bits or parts that are made for Land Rover so that it will hold some value but do mind you will not what you spend for them. I will not comment about putting Jap parts etc.
Best bet is swap it with Discovery gear but again you will need special conversion kit bits for gauge cluster, trim etc
and also this will work pre-2007 models as old Discovery 200tdi 300tdi engines could be planted to defenders with the auto gearbox.
There were NAS spec and specialist UK models sold factory auto but are uber rare now.
All in all its a very tedious and expensive job, not worthwhile doing the crime to a serious off roader, as plenty of SUVs in the market with auto transmission, but if you still want the looks and auto, All the specialists in the Country may be able to handle, provided you save a buck by getting down the internals.
Also if the heavy clutch is your issue, there are plenty of kits to add a servo unit to make it feather light!