I don't have any experience of using either an overdrive or a modified transfer box, but I am sure the modified transfer box would be more efficient than an overdrive, as an overdrive will introduce additional friction to the transmission. I think that one of the reasons that (proper) 4x4s are so bad on fuel is that they have, in effect, 2 inline gearboxes and so the mechanical friction is twice as much as a normal gearbox. Putting an overdrive on, is adding a third gearbox - which will make things 3 times worse.
If you only use the Land Rover on the road, and both axles are Rover type, then Range Rover diffs might be worth considering. I think you could find them very cheaply. The down side is that low ratio gearing will be raised.
I think the most cost effective option is to not modify the transfer box or put an overdrive on - I just stick to a max. speed of 50 to 55 mph, except for overtaking. I am a believer in electric cooling fans though - as well as saving fuel, I've found they make the interior heater work better. I reckon that taking off the rear mud flaps (if fitted) might make a bit off difference to fuel consumption as they must make the air resistance worse.
I think there is a good argument for not making a series Land Rover faster: The 50's technology suspension, steering and brakes are not really up to it.