Now, at the end, I can say we carried everything we needed plus a bit more.

This "everything we needed" part is what we are a little proud of, as the selection of the equipment was a fruit of cca 10 years of overlanding experience.
We made the "furniture" for the vehicle, it was equipped for two not too demanding or picky adventurers. Some photos of the interior:
http://www.landcruiserclub.net/forums/showthread.php/39560-Hello-from-Vrecha/page2
The equipment was relatively basic according to the popular show-overlanding standards. We are very much "Tom Sheppardish" regarding the equipment. Carry less, know more.
For example, the first aid kit was custom-compiled by us, but we knew how to use every bit of it properly as we went to a five-day emergency First Aid training course and passed the exams.
What we don't know how to use, we don't carry with us.
Another important variable was also that we knew we would have enough time (we don't drive today so popular "amateur rallies"), so we could choose the equipment that is maybe lighter, packs better, but handling with it requires more time. The rubber mats instead of big steel or plastic plates for recovery come to my mind in connection with this philosophy.
All together, when going to really remote places, the simple logistic rule apply:
water(+food) = time
fuel = distance.
Regarding time, we were equipped to survive cca two weeks completely on our own (usually we spent 5-6 days like this, max was 9).
Regarding the fuel, we could cover cca 1500 km of normal desert terrain (moderately difficult pistes, as Nema-Tidjikia for example). For the really rough overland driving (Mauritania out of pistes, soft sand and difficult dunes), we could cover cca 700 km of terrain like this. Here we see a need to add one more fuel tank (cca 100 l) so in future we will be able to dive more comfortably into exploration of the long pristine desert traverses.
All in all, I'm a little proud of the fact that our HDJ81, fully equipped and loaded with fuel and water weighted "only" 3100kg, which is still very near the factory GVW figure. And it performed marvelously on demanding desert terrain.