Your concerns about airflow in back bedrooms are important. It also elevates the job from simple AC install. Do you have any info on how Contractor A proposes to address that?
Contractor B sounds like he might have potential, just that he has not been as thorough. Perhaps pushing R22 because he is not as comfortable working with R410.
Your contractors C, D, E... sounds like you have written them off, with reasonable cause.
Best of luck -- Pstu
PSTU'S statements should not be considered representative of this forum as he is only a well read HOMEOWNER who means well but has not been known to get it right every time.