Such a great question and a lovely example. Yes, you can put the entire bulk in the refrigerator to slow down the process. You can easily buy yourself those couple of hours and resume. Upon resuming the process may move a little swifter, or a little slower depending on temperature and how the dough has advanced. So watch the dough. Using the new Modern formula you should be able to look for the signs of development vs. managing time.
You can also shape and proof in the refrigerator. In terms of which is better. Hard to call, both work. I think I prefer, with this loaf, the bulk cool retard. I find that to be a little more flexible. But both work. In the event your loaves “overproof” in the refrigerator, just dump them back out on the counter, reshape and then proof again on the counter.
Say you’re at the bulk fermentation stage and you suddenly realize you have to go a 7 year olds bday party and won’t be back in time for the next two stage. Can you refrigerate now and pick up shaping in two hours? Or get through bulk fermentation and refrigerate during proofing?