I merely disagree that the Iraqi Government will join in such a war since they are too busy with internal issues and their military is hardly ready for war.
If Ayatollah Sistani and Khamenei say: it is war then it is a holly war. The internal problems will be of secondary importance!
US has never dealt with a populous shia uprising. Even without fatwa, there will be hundred of thousands of volunteer going to Israel! With a fatwa, the numbers goes into millions of young men willing to die!
I do believe that if Israel attacked Iran, that there would likely be many (thousands) of young Shia men who would be willing to fight Israel and journey into Syria and Join the fight (assuming Syria invades Israel after such a strike),
Based on what analysis you come with this ridiculous low number. I am telling you, we will have at least around 200,000 regular Pasdar and Basij willing to go though Iraq/Jordan and Syria/Lebanon to fight. Volunteers from Iran is a in million range!
Only volunteers from Iraq will be more than your estimate, not mention Palestinians in Jordan who want an excuse to join in!
Come out from La La land of superpower mentality and smell the roses!