Hard-bottom no-knead bread

One is that it might be helpful to see what the crumb looks like and how thick the bottom is. Also, when you say it's hard, what kinds of bread are you comparing with? 

Have you checked the temp of your oven? If it's hotter at the bottom, that may (help) explain your bottoms being harder. You can try raising the rack that the DO sits on, if there's enough headroom of course.  If you've been putting the DO right on your heat blocker, you can also try putting the blocker one rack below. 

Also, you can soften the crust, top and bottom, by putting the loaf into a plastic bag after it has cooled. Other enclosed containers should work too provided they're not too much larger than the loaf. 

the first thing to check is the temperature of the oven. I had the same issue with my No-Knead and finally resolved it buy preheating the oven to 500∘ F, then dropping it to 450∘ F after having closed the door for one minute. I also placed a heavy cast iron griddle (the kind that covers two of the stove's burners at the same time) on the rack one level below that rack that the DO sits on, so I believe that the bottom side of my DO gets more even heat. My loaves not come out perfect on the bottom, no more thick, scorched bottoms for me.

Try one bake in a cold DO with a pre-heated oven.  Put the dough 15 min sooner into the Dutch Oven and add 15 min baking time ahead of your normal baking time.  --the time it takes the DO to heat up.  And put it back in the middle of the oven, where the top edge of the pan is closest to exact middle.   Electric oven?

The baked loaf looks like the dough was proofed in a basket, seam side down.  Correct?  Did you cover the top (bottom of the loaf) with anything to keep it from drying out?  Perhaps it dried out and then hitting the hot DO turned the crust to crackers, tough ones.  What do you think?