Boeing is not responsible for company SOPs,however if requested they can give an airline its opinion.
The stab trim setting is on the before take off checklist.My sops dictate to set it when the trim is crosschecked with the loadsheet and fmc.
The v2 is set in the same way,as the speed are entered into the fmc,and just before engaging the autothrottle.
Both pilot will perform these duties together in order to avoid any finger troubles..
Sops vary from airline to airline.
Concerning the air system, indeed the only after start check is to ensure the isolation valve is set to auto.
It is however good practice to follow the pm during his after start procedures.
The after take off checklist(boeing) ensures pilots check bleeds and packs are in the proper postion.
Obviously pilots should not wait for altitudes above 10000 ft (in case of a high transition altitude) to perform the checklist.
A check of slightly cabin climb rate is a good idea and could be some airlines sop.