Got it. NYT no knead is a great recipe for simplicity but uses brute force (aka a lot of yeast) to make things happen quickly. A lot of yeast + a warmer than average kitchen can lead to a dough that gets slack fast.
I have three suggestions:
1) After 2-3 hours wet your hand and reach down the side of your bowl or container, grab the dough, gently pull up and then into the center of the dough mass, then push down. Rotate the container 45-90deg and do this again for a full revolution. Repeat after 45 minutes. This minimal amount of work starts forming a gluten cloak and you will see a big difference in the consistency of the dough - it will be more cohesive and have a tighter skin which will prevent it from flattening out as much before baking (something like this, but take your time:
https://www.instagram.com/p/BINaj_4ABQL )
2) After shaping, proof in a banneton or some sort of basket and bake in a cast iron pan or dutch oven or dutch oven lid. These will naturally limit the amount of spreading your dough can do
3) Consider trying an overnight proof - use just 1/4t of yeast instead of a whole packet and let the dough go for 12hrs (or up to 7 days in the fridge). This is the basis for artisan bread in 5 minutes a day
Also, the NYT original recipe was a bit undersalted - I would increase the salt to 2t for 3cups of flour.