Hey there, nice example... here we go.
First, there is no +3 attack modifier for cargo transports. In trying to figure out where that come from, I'm guessing that's based on the line "target transporting battle armor" at the end of the to-hit modifiers table. That's a sub condition under Anti-'Mech Infantry, and applies only to Anti-'Mech Infantry attacks (where infantry swarm a unit). If the target of an anti-'mech infantry attack is carrying battle armor, those infantry are going to have a hard time swarming it.
For TMM, the transport never affects a transported unit's TMM. TMM is based on movement mode selected. Note that errata clarified that a transported unit cannot choose to stand still.
Revised: MAS is based on the standstill mode. You only get the bonus if the unit used the stand still mode. You cannot use stand still and be transported (see errata). So you can't get the MAS bonus any turn you were transported.
Battle Armor, when a target of an attack, have a +1 target type modifier (to-hit modifiers table, bottom left column under target type modifiers).
Battle armor (along with conventional infantry) are not affected by movement mode modifiers. (This was errata, found in the footnote of the to-hit modifiers table for the movement mode modifiers). So battle armor do not take a to-hit modifier if they jump, or if they stand still.
Most recently compiled errata for AS, that includes transporting, movement modes and to-hit modifiers is found
http://bg.battletech.com/forums/index.php?topic=31693.msg737437#msg737437