The only thing I can think of is to use plastic or epdm pond liner down the side all the way to the bottom. Even if you counteract it with sulfer it will continue to release small amounts for some time to come meaning that amending with sulfer maybe an on going thing for longer than you may like. Probably not what you want to hear but it all I can think of at the moment. Maybe someone else can offer an easier solution to your challenge.
Good Luck and Happy Growing David

I agree with david. Fully line the inside of the bed, and while your're making the adjustment, stucco the outside of the blocks for cosmetic reasons.

Question..are you sure it's sweetening your soil, and is having a negative effect on your plants?

I agree that I would wonder if it a problem of itself (too sweet) or is there another problem that is unrelated to the concrete itself? Answer this and you can plan your approach based on real as opposed to possibly percieved need. Everyday ph paper from a pharmacy will allow you to test next to and middle of the bed and see if the sides are a higher ph value than middle which would tell me that leaching is occuring and may pose a problem. This is of course based on the premise that the media in the bed is all equally and throughly mixed end to end, side to side.
Good Luck and Happy Growing David