Over the past weeks I have learnt a reasonable amount about how the air suspension hangs together and what causes what errors. There are others on here with much more knowledge as well.
What is required is the fault readout, once we have that isolating it will be easier.
A simplified layout is
Pump -> Valve -> Compressed air cylinder (with a pressure sensor on it) -> Front & Back valves -> Air struts + height sensors
All ultimately linking to the ECU.
The fault code will help pinpoint where the error is occurring. I have some software called Allcomms - I bought it a few years back to reset my codes when I renewed the piston ring in the air compressor (I got another 20,000 miles out of it before the cylinder wore too much) - it costs but if you intend or have to do a bit of your own maintenance (I personally find it quite rewarding and it is just lego) then it is worth it.
All that said, don't worry about it too much. As long as the car rides evenly and air is retained in the struts it is ok to take your time - I ran for 8 months with "Air Suspension Inactive" and a trip to southern France. I'm not saying just forget about and it is disappointing especially on top of the alternator but you can relax about the issue (others may disagree).
My problem was actually a £40 sensor on the compressed air tank. It wasn't telling the ECU that it had reached pressure and thus the system decided there was a leak 'Pressure Resevoir Static When Filling'. I had terrible pump output but with AllComms I could locate the problem.
I'm in Broadstairs, Kent so too far away but there may be other kind members with a diagnostic kit near you. If you don't want to diagnose or fix it yourself then go to an Indy LR garage (as you have said) and get a list of the faults and post back here before you act on any repairs.
Charlie
p.s. it really does sound like the steering lock to lock you have to do after disconnecting the battery. I know you've done it but....
p.p.s I had a possible alternator issue diagnosed incorrectly by a garage 5 years back. The answer was to replace it - as you have seen they are not cheap. I got the garage to remove it and I sent it to:
Unit Exchaqnge
All the bearings were replaced as a matter of course however there was nothing wrong with it. I'm not saying yours was 'not' faulty but my repair (or lack of it) was £75 and output was bench tested. I'm mentioning this because it may be relevant to others with respect to not just defaulting to replacement. The alternator that was 'written off' has since done 50,000 miles...
Charlie