The 10% rule of thumb really sucks in the states. The Range Rover MKIII (and I think LR4) has a 7700lb towing capacity, but a tongue weight rating of around 550lbs. You could easily get a Euro-caravan in the 7k range with a 500lb tongue if they center the axles right. Try finding one like that in the states? No way. 10% minimum, meaning 5k travel trailer tops.

. If you have a slide, you are looking at 600~700lb tongue weight on a 5k trailer. Not a problem at all for my 2500HD (it loves it), but it sucks when I want to camp in one vehicle instead of having my wife drive behind the truck in the overlander.
To the OP, the tongue weight is going to be your limiting factor, but if you are only loading the trailer to 3k, you should be fine unless your batteries are all stacked on the front a-frame

.
Try to find the local scales in your area and test-weigh your first loads. It will make the math easier and far less "academic", which can have huge errors. You should be able to easily decipher the weight over the trailer axles, rear axle of the LR4 and the front axle of the LR4.
Axle ratings for your trailer can be easily determined, and the rover's should be on the inner driver door.
GCWR is the total rating of the LR4 and the trailer. Stay under it.
Each axle weight should be less than the rated axle. Any cargo you put in the LR4 will be distributed on these numbers. If the rear rating is over and your front has capacity, move more batteries in the front seat or front bench compartments to get them on the front axle. it IS possible to be under your GCWR and GVWR but OVERLOAD a rear axle. Many believe you can "fudge" the other ratings, but do NOT exceed an axle rating (and by not exceeding an axle rating you won't exceed GVWR. You could exceed GCWR if your trailer tongue weight is light and the trailer is heavy, but as mentioned earlier in the thread if you know what your doing it may not be an issue......exceeding axle capacity IS!
Again, GVWR is just the sum of your axles, so it won't be exceeded if you stay under each axle.
If everything clears, I wouldn't stress too much about tongue weight. Honestly, is the LR4 hitch that bad that it can't take 700lb tongue weight? I thought I've seen a thread where the hitch itself says it's rated for more than that. Why the 500lb rating? Air-springs?
ALSO:
If the numbers check out, make sure you have enough inflation for your tires (their ratings are on the sidewall). If you have "weak" tires, you might be pushing your weight rating with an empty LR4, so don't even think about a trailer. Sadly, lots of 19" and 20" tires are junk. Land Rover should be ashamed for putting that rubber on such a heavy vehicle, much less an off-road one. If you have aftermarket rims, you may want to find your receipt and look for their weight ratings. Some rims are made for mall-crawler SUVs and cars looking for the "hot wheels" look, and they may not be rated for much more than your empty LR4. Stock wheels will be rated for your axle/GVWRs; again, stay under these numbers.
You may need LR-E tires, which should be just fine (I believe some people make 20" LR-E. I would assume 50-60 PSI for a full load like that, most manufacturers of LR-E tires have inflation/weight ratings in PDF format for download.
Then make sure you have a break controller with trailer breaks and you should be JUST FINE.
Honestly, doing it "virtually" is a waste of time. What if your batteries weight 26lbs. or 27lbs? You could get into trouble fast. What if the trailer weighs 1000lbs empty. Or your LR4 is pushing 6000lbs with a full tank of gas and your butt in the driver's seat. Now your disco's capacity is much less than listed in your owner's manual.
Go to a scale. Do it right. Some are free, but even a CAT scale should only be $10 or so.
Good luck!!
I'm being VERY conservative here, as not everyone is comfortable with lower tongue weights.
Over on RV.net, I get blasted for even suggesting 10%, some folks think anything less than 13% is a "death trap"...
Personally, I've yanked 130,000 lbs B-trains all over the BC rockies, so I'm fairly comfortable with trailers.