There is not a way around it that I know of. To put it in perspective, what is the cash value of 18,000 miles, about $180? Your landlord (and anyone who accepts credit cards) has to pay at least twice that to the credit card companies just for swiping your card. Consider that the landlord would likely pass that on to you in the form of higher rent. Yay! Now you are getting a discount for paying cash that is better than using your card for points! You're welcome.
It's only $180? I guess I never thought of it that way.
A free roundtrip flight to the Caribbean or Mexico is 35,000 miles...just by paying my rent with my card I'm halfway there to a free flight in 1 year...and I'd get there in one year because I'd also be putting $1,500 worth of non-rent charges on the card.
However, if I don't pay my rent with my card, I estimate it would take 2 years to get that free trip (without putting $1,500 rent on the card I'd expect to only put about $1,500 on the card a month as opposed to $3,000 on the card a month).
So I was looking at it from the perspective of...by my landlord simply not taking credit card payments, it will take 2 years for a free flight that would under other circumstances (like the one I'm in now where the landlord accepts credit card payments) take only 1 year.
Wrong way to look at things?