The hot restart problem is not exactly as you are viewing it. The fuel pressure comes to peak in a second or two. It does this the same hot or cold. It is very likely that there will be no pre pressure when starting cold.
The difference is vapor locking. When the engine is hot the heat is transfered to the pressurized liquid gas. Whether it boils or not is dependent on the pressure. The fact that you take longer the longer you wait when hot, probably isn't an indication of pressure. The pressure probably leaves in the first minute or two. From that point the time interval increases the heat transfer and the boiling of the fuel. Typically the problem is the pressure accumulator but a proper leak down test should be done.
Bosch Master, ASE Master, L1
33 years MB technician