4.6 v8 problem starting

hello, I currently own a 4.6 V8 (R reg)

In a morning the car starts up perfect with no problems but then I go on a drive, turn the engine off and when I come to start it it really struggles to start. I've put a battery on off a TVR on it with really high cranking amps and that still doesn't solve the problem. I've done a mini service on it as well, and still the same. Some times I've been trying to start it that much it's ended up killing the battery. The altanator is working fine as well. Hoping some one could give me some info on this situation? It's also got lpg and that doesn't work because it keeps saying low pressure.

Cheers

if it only happens when its 'warm' could be full starvation, have had old machines that has this issue where badly routed fuel pipes caused evaporation. (altho I appreciate the fuel injection may not suffer from this).
maybe worth doing a compression test when cold then comparing when engine is at operating temperature to rule out any minor warping with heads. check manifold gaskets etc, when it struggles to start, try get something like a smoke pellet and offer it around the manifolds / air intakes to see if any air is getting sucked in elsewhere

try pulling a plug out when its difficult to start to see if a plug is wet, this could help show if fuel is making it through