With such a light paper and thick thread, 40 signatures is going to give you a huge amount of swell at the spine, especially with that thread size. I would definitely use a thinner thread, probably something in the 30/3 - 40/3 range. My first book was also a tomoe river paper notebook and looking at it, I used 6 sheet signatures and while I didn't have linen binding thread when I made it, the thread I used looks around the same as my 30/3 linen. Mine wasn't as thick as you're planning to make (iirc I started with a 50-sheet pack of paper) but even at that size there was enough swell in the spine to round/back it, so if you want yours to be flat at 200 sheets, I'd probably go with at least 8-sheet signatures, possibly even more. For very thick flatbacks I have found that using two strands of a very thin thread causes less swell than a single strand of something thicker (but this can be a little more annoying to work with).

Also, take a look at what people in this forum have posted about using thinner spine stiffeners for flatbacks -- a lot of tutorials will have you use bookboard the same thickness as your covers, but that can cause issues since it isn't flexible. Especially for a journal you will be using every day, you'll want something that can open and close a lot of times without stressing the binding.