You're not making 1 cent more with VGC->MO->landlord. There is no such thing as getting a rebate for paying your rent or mortgage.
Choosing CC->AGC->VGC->MO->landlord instead of CC->AGC->VGC->MO->bank is the same exact profit. You don't make any extra with this. You make extra if you get the landlord to swipe your credit card for free. The only benefit is to avoid another MO deposit at the bank because you have too much MO/cash this month.
Also depends what you are trying to optimize. The real steps in your process are cc->AGC->MO->bank followed by check to landlord. The first option avoids this last step (as well, as you point out, the need for another MO deposit)