I had same kind of issue with a Allion.it was completely random some times runs all fine but some times engine stops as soon as i start...had no issue in high speeds but in traffics it was a headache. ..but finally my mechanic said it got to me the fuel filter located inside the fuel tank and mechanic showed me all the gunk in the old filter which surprised me about the quality of sri lankan fuel.replaced with a genuine fuel pump filter & Now there is no trouble at all...
1.But as u said u got no idle issues as i did so before going for any other repairs try to jump start thinking ur battery is dead...if it starts without any trouble u can make sure it was a issue with ur battery(u can check if ur battery voltage too, it got to be over 12.5 to assume its healthy to start).may be battery is fine but faulty alternator...but if you still find it difficult then you can go for more deeper diagnosis...
2. some vehicles got clutch switch/brake switch which completes the ignition circuitry to let the vehicle to start (in the vehicles where u need to press clutch/brake when u ignite) some times when those switches get faulty starting issues are present
3.I have some times seen mechanics hammer tap the started when there is no turning over but clicking and it some times simply works like a charm so u can check for that too
so hope those would be useful to diagnose ur issues...