Hi GreenVogue!
I would love to help you out with your battery drain if i can, as i know how it feels as mine 4.4 V8 had a constant battery drain when i purchased it earlier this year. Out of interest has your car had the 07 spec headlights fitted? after weeks of searching and performing test on my car I found the drain which was being caused by the 07 spec facelift and new style headlights the previous owner had fitted.
With regards to your battery could you check what size the battery is, is it a land rover genuine battery or a after market model? The battery spec should be at least 110Ah & 850cca (cold cranking amps)
The HVAC issue is caused by the HVAC final stage resistor, if they have only changed the relay AND NOT THE ACTUAL RESISTOR this may still be causing an issue, does your fan still come on on its own??
If your battery has been drained completely over and over again, this may have ruined the battery and may need replacing again, do you have a plugin battery charger as jump starting the car will not recharge the battery, if the battery was quite flat then it would take a very long time for the alternator to recharge the battery to a sufficient level. Get your self a plugin battery charger and connect your battery up and charge it until it is fully charged. You can check the condition of your battery by using a multimeter to measure the volts in the battery it should be 12.4 volts but anything over 11 will start the car, anything below and it will not start.
Another issue to check is that the alternator maybe faulty and causing a loop back which would drain the battery very quickly.
Just to confirm so you are aware, when you lock the car it takes around 16-20 minutes for the car to go to sleep, i.e. the 'car' you refer to is actually the BCU (Body Control Unit) that has to go to sleep. When the car is 'awake' it draws around 700mA which if it is not going to sleep would drain the battery quickly, when the car is 'asleep' the entire car should not draw any more than 20-30mA.
Sorry for the long post, but i know how you are feeling, and once i sorted it out its a great feeling!
Matt