Additional testing: Rome besieged on turn 4. Once again a bit of luck from the beginning: two Macedon Aid cards on hand. However, it does seem that no other opening maximizes the use of these cards as much as this one. So, additional thoughts:
1. It seems to be safer to move through Gaul with 10 units or less. I usually take 11-12 units with Hannibal and suffer minor attrition. 10 units caused no attrition whatsoever, both when crossing the Alps and then doing an extended move without card to Umbria.
2. You do not have to take any cities in Umbria on turn 1. I had to assault two minor cities on the way there, but did not attempt to take either Ancona or Asculum. I was content with merely denying Umbria to Romans.
3. Roman first turn will see a Roman army in Placentia engage Hannibal and the one in Genoa attacking Africa. Leaving enough units with Hasdrubal in Spain does seem to force Romans to take a stab at your own homelands. Early Roman invasion of Africa is to your advantage since it will be conducted by lower ranking general. Unless Romans play a Numidian Revolt, their army will be outnumbered by combined Carthaginian-Numidian forces allowing you to score an easy card or two.
4. You have plenty of options on turn 2. Safe way is to subjugate Umbria (made easy with decisive victory over Roman army during Roman turn 1). A riskier, and potentially more rewarding option, is to storm Tarentum (always with a general and extra unit) and two minor Apulian cities. This denies Romans further recruitment in that province, grants you 2 units in reinforcements at the end of the turn and an extra card, of course. Umbria is easily recovered next turn, if needed.
5. Third turn usually sees the defeat of the Romans in Africa and Himilco sailing to Tarentum. Hannibal can either move to Umbria or Bruttium (preferred). Hasdrubal moves to Cis. Gaul (joined by Mago from Gaul?). Requires a bit of luck with Senate.
6. Fourth turn - Rome besieged. If Hannibal on the Move is available, Hannibal can trounce an extra Roman army before proceeding to siege. At this point, with one Roman army either engaged or defeated in Africa, another defeated earlier in Umbria and scarce reinforcements due to early loss of Umbria and Apulia, the Roman state can hardly afford to field a serious force. The end is 1 to 4 turns away.