Well, I made some attempts to fix them up, and it seems like it worked! I made up a putty of fine sand and lime putty and actually painted it on with a brush:
Then I wiped it off after it dried a bit, which left the stuff in the crack. Then I went back with typical whitewash and painted over it 3 or 4 times, doing the standard wetting it down and wiping it down between coats. It turned out GREAT!
You can't even see the cracks in person, let alone these photos!
Check out the front of the living room bench, even from the photo above!