I can't get this recipe to work for me. Will it not work if it's too cold?

Thanks Lori! I have tried the float test with my starter each time and only use it to make the leaven if it floats. I've been really pedantic about getting the starter healthy so I don't think it's that. I seem to be getting up to the point of final shaping and the whole thing is still just a cold, sticky flabby mess, even after 10+ hours of bulk ferment. I haven't tried a float test at that stage though. If it doesn't float at that stage, what do you suggest by more "attention"? Is it possible to give the dough too much time in bulk ferment? Is the cold at least a reason why bulk is taking so long?

The float test is confirming your starter is good, but what about the leaven? Though rye is generally a fast fermenter, it may be conditions in yours simply need more time to build the numbers of yeast up. I'd do a float test of the leavener before moving on, just to be sure that's ready. One other thought occured to me, which concerns your water. It is best to use a bottled or filtered water for baking, because treated water can contain things that can kill yeast. It's also possible that there is a problem in the bulk stage during the folding and stretching process. You are developing gluten- but also redistributing yeast and helping reduce alcohol pockets, which would kill the yeast. It's also entirely possible that it is going too long in the bulk ferment, yes. There will be too much alcohol and gas produced for the yeast to continue to live, and the dough will collapse. Without the yeast producing gas, there's nothing to inflate the dough- so you have the flabby mass. So perhaps the problem isn't that the bulk is taking too long, but that it is being given so long or there is a problem with the leaven.
So far as attention- I simply meant your bulk ferment might need more folding and resting time. It's also possible you are giving it too long, and the yeast is dying because there is too much alcohol and gas in the dough.
Dough can over proof in either the bulk or final stage- leaving you with a dense bread. It's trickier to make bread in this way- which is why more folks don't do it. You have to figure out what works best in your kitchen, in your particular environment, and with your ingredients. It can take some time, and multiple batches to fine tune that.
Yeast actually likes it on the cool side, between about 27 -35C I've found. So unless your kitchen is really a walk in refrigerator, I still rather doubt cold is the problem. Next time you do the bulk rise, start doing a float test each time you do the fold. That should give you a better idea of when it's ready to move on to the final stage.

Hi Lori, Thanks so much for the detailed response, thats super helpful.
I'll try with filtered water, makes sense... actually if that's what it is, that's fairly vital information I haven't considered until now. I'll also have a go with the float test at every stage. Thanks again!

Hi Lori,
Little update, still no luck using filtered water.
My starter passes the float test, as does my leaven.
After bulk ferment for 5 hrs, the dough looks cohesive but never really rises significantly, maybe only a tiny bit. Some bubbles form. The dough at this point doesn't pass the float test. This is why I've experimented with shorter and much longer bulk ferment times.
This time I felt like the dough was a bit more cohesive in final shaping, but it was still very sticky. After resting overnight in the fridge, it stuck to the basket again and came out looking very misshapen, and collapsed into a pancake shape on the bench pretty much instantly. Was impossible to score as it just stuck to the blade.
Could it have something to do with the hydration in this recipe? Sort of coming to my wits end here and wanting to give up.

Yes, it could well be a problem with the hydration percentage. It may be that you need to knead in more flour before it goes to the bulk rise stage. With this sort of bread, a lot of gluten development is necessary or it won't be able to retain the gas produced by the yeast once it no longer has the support of the basket. As far as sticking to the basket- I did not ask, but do you have a muslin or linen liner? I don't care to do rise in just a plain basket, because it does tend to stick badly. You really have to be generous with the flour - and I actually rub flour into the muslin I use as well as give it a generous coat. Once you tip it out, you can use a pastry brush to remove excess if you think you need to. Actually, I would probably knead the dough prior to the bulk rise until it is pretty much not very sticky. I wouldn't blame you for giving up, but I encourage you to try again. This time, do your float tests, and knead that dough until it's not really sticky. Heavily flour the basket, consider using a floured muslin liner. That should give you the results you hope for. And if in the future, a dough refuses to rise- you can always mix another teaspoon or so of yeast in a bit of water, and knead that into the failed dough. Give it a bit of time to rise- and you can often save the bread. It will be a bit more yeasty than an ordinary sourdough- but still a good loaf. Baking sourdough can be a challenging skill to acquire, and it can seem impossible- but if you stick with it, you CAN do it. Don't be discouraged by a few flat loaves. We all had to produce our share of bread bricks before we produced loaves we wanted to show off and share. Anyone tells you different isn't telling the truth.

Lori, thanks for the reply and words of encouragement. I appreciate it!
I'm using a basket without a liner (don't have one) but have been seasoning it very generously. I'll keep at it.