Here is a question for you. How long has it been since you got the new fridge? The reason I ask is because the seller should be able to bring it back to the store if you didn't wait too long to say anything.
Sounds to me like you are really trying to be a nice tenant...but you really do deserve a fridge with the rent. How's the bathroom?
I've had the new fridge for about 3 weeks now, though I didn't install it myself until about a week ago.
Does this mean that the fridge, or the kitchen itself was incorrectly installed?
It is your right as a tenant to have working appliances.
If your landlord is unwilling to fix the underlying issue, which you think is the kitchen design, check with the San Francisco rent board.
It might be that you will have to fix the problem yourself and deduct it from the rent. But check first before doing any work.
Hope that helps!