Two things spring to mind. One is questionable but I'll say it anyway...
As I started to read your post I wondered if there was a vacum building up in the petrol tank. ie - does it run better with the filler cap off or does it make a sucking noise when you remove the filler cap. If the tank can't breath then it will eventually start the fuel through suction. I'm not sure how this would afffect the engine on LPG.
Secondly - I once had the same sounding issue in an old porsche 911. It would start from cold no probelm but as it got warm it would start to die then it would stop and it wouldn't start again till it was cold. I tried everything and I eventually discovered when I changed the distributor cap and rotor arm it solved it. I figured that as these items got hot they wouldn't conduct electric as good and the spark got weaker and weaker till it stalled. In fact I think I just swapped the to rotor arm from memory...??? anyway its just my two penath worth of experiance.
Good Luck
Richard

First off, if you can find a rotor arm on your RR you are in trouble.....
As the problem is the same on both GAS and Petrol, it is safe to assume it is a problem on the sensor side of things. I would first look at the MAF. Try swapping it out for a different one. These arent the most reliable of things and rely on a pair of heated wires to measure the air flow. Sometimes a good clean with carb cleaner will work, other times not. Its also wworth getting The ECU reset to factory defaults before carrying out any diagnostic work, as the ECU may have been compensting for a failing sensor. Next check the Lambda sensors.