Michog:
Wow, I don't want to be negative, cause I have known folks with great experiences with DII's, but by and large, ... MOST I KNOW WITH ONE, have had bad experiences.
My sister and her husband both had 04's - both white/tan one an SE7 the other an SE. BOTH had head gasket issues at 74K miles. One had a brand new LR crated 4.6 installed and never did do right after that.
I sold a DII to someone on Expo here after mine had a slipped liner (more in a moment on that). It had a brand new motor with warranty from Land Rover North America installed. Two months after the warranty, his motor blew ... and he basically took a HUGE bath trading it on an LR3.
You may consider exploring the LR3 as early ones can be had almost as inexpensively as an 04 DII (which have lately seen an increase in price).
The secondary challenge with a DII outside of the Head Gasket is a slipped liner. (even more common). The sleeves on the cylinder walls are made of steel. The block is aluminum. If you even slightly overheat that engine, the aluminum expands, the steel sleeve does not, and drops. Hence, you have toasted a motor. The later 4.6's (if you can A) find one and B) afford one, had corrections made to them with a "ledge" to hold the sleeve in place in case of overheating, but that inventory of replacement motors is dwindling.
If you buy a used motor (even a low miles one), know that you are in for the Head Gasket replacement or a dropped liner at some point in the future, and start your repair savings account now.
FYI- The truck that I sold that had the new crated 4.6 motor in it, ... the replacement motor installed cost $9800.00!!! (almost the value of the truck).
D