The only way to sort these sort of problems is to methodically go through each system on the engine until you are confident you have covered all the possibilities.
This would be my suggestion of a work menu:
1 Fuel system
Stale fuel, even when diluted with new, is known to cause very bad running with unpredictable symptoms. I would drain all fuel from the car and start again with fresh.
Renew the fuel filter
Make sure you have enough fuel in the tank to cover the fuel oulet to the front of the car. Main tank runs out at about 1/4 tank, at which point you need to switch to reserve tank (pull the knob below and left of the radio position). There is only one fuel space in the tank, but two pickups set at different heights in the tank.
Take the plugs out, uncouple the pipe to the first carburettor and motor the engine on the starter motor. Check that you have a good supply of fuel flowing out.
You should have HIF type carburettors. The float chamber is under the carb. Check that you can blow into the fuel space when the carb is empty. Check that the fuel shuts off when you raise the float. Check that the float isn't puctured - ie floats in water or fuel.
2 Ignition system.
Check that you have the plug leads on in the correct positions. This isn't always immediately obvious. Set the engine at compression stroke on no 1 cylinder. (both valves closed, piston at TDC judged by a pointy thing down the plug hole) Take off the distributor cap and establish which lead pillar the rotor arm is pointing at. Trace the lead from that cylinder and see which plug it goes to. If wrong, correct and then position the reamining leads to match the firing order.
Renew the plugs
Then check that you are getting a spark at each plug when you motor the engine with the plugs out.
If the engine starts and fires OK whilst the motor is turning the engine over, but then dies when you release the key to the running position, you could have an LT fault. The P6 has a ballast resistor in the loom to drop the normal voltage at the coil to around 7V. When the starter motor is operating the feed to the coil goes via the motor and raises the coil voltage to 12V. Likely causes are a fault on the ignition switch or a broken wire somewhere in the system. A temporary check would be to feed the coil from another known 12V supply. But don't leave it like this as you will burn out the coil. It doesn't like 12V conntinuously.
Check that the coil is the correct type. Perhaps someone has replaced it with a 12V type instead of a ballasted type?
You can get some very peculiar symptoms from defective chokes / capacitors in the distributor. Yes, even brand new ones, in fact especially brand new ones, as there have been some dodgy batches of Chinese made ones around. HAve you got a nice old Lucas one in a tool box somewhere?
Then we are on to peculiar ones.
The inlet manifold is flexibaly mounted. Check that the O rings that provide the air tight seal are in good condition.
rebuild carburettors(!)
Check that the vacuum hose to the servo is in good condition and not drawing air.
Check that the vaccuum pipe to the distributor is intact and not drawing air. Suck on this pipe and make sure that the base plate of the distributor moves in response (vacuum advance retard)
Make sure that the distributor base plate will rotate and spring back to the original position (centrifugal advance retard
Hope that lot will keep you going for a while and get you somewhere near!
Chris