Should note that you have an aftermarket ecu installed. Has the tune in the ECU been verified to be good? Unfortunately its a complete can of worms, being a modified car. That is something that noone tends to mention to people that are buying a modified vehicle, that invariably something will go wrong or play up and a certain level of technical nouse is required, or deep enough pockets to go pay a good mechanic.
The issue could be one of a number of things. Have you tested spark quality and operation of fuel injectors? Jam a timing light on the car and crank it over. See if you are getting pulses when it should be trying to fire. If you aren't there could be some wiring issues or a dirty crank or cam angle signal to the ECU. The reluctor type sensors in earlier toyotas can be notoriously noisy and sometimes ECU settings need changing to filter out the noise. Someone should also have a look at the tune for you and make sure its all AOK, safe and there are no major flaws in it. Cold start are one thing but if you are having issues on hot start there would need to be some dramatic issues in the tune. Cars actually aren't that fussy when it comes to starting especially with a warm engine, fueling doesn't have to be EXACT so any errors would have to be vast so I doubt this will be the problem.
Vacuum leaks shouldn't cause too many issues as I would suspect your car doesn't use an AFM anymore which is what is generally sensitive to air leaks. MAP setups aren't as sensitive when it comes to vacuum leaks.
It is harder to start under any specific conditions? Or just all the time.