Ok, so here are my attempts to use your stats to craft the item on a simulator using Rath's rotation:
I have chosen to eat an HQ Baked Onion Soup, so it adds 48 CP and 28 craft. I have used 3x CZ here (which adds 42 CP in total). I took two trick of trades along the way (another 40 extra CP), and I managed to squeeze out 11 touches. If we assume 2 failed Hasties, we will have IQ10. And yet you can still see that I am 6 CP shy at the end to use the Byregot (and then 1 more CS II would finish the item). Obviously, your 382 base CP is just a tad bit lower than what you need to use this rotation.
In order to squeeze out more CP, we can either overmeld a bit more Cunning Materia, or we can count on taking an extra Trick of Trade (which entirely depends on luck), or we can somehow modify our rotation to squeeze that that CP. We can change two of the SH II into SH, which will give us the necessary 6 CP. But instead, I have chosen to abandon the 1st SH that wraps the PBPs, which buys us an extra 22 CP:
As you can now see, the rotation is pretty much the same. But we now have 22 extra CP, which makes up the missing 6 CP to use the Byregot. However, there's still 16 CP left, and it's a real pity. Because 2 more CP, and we'd have been able to fit in an Innovation, which will wrap a Hasty Touch as well as the Great Strides + Byregot. If I were you, I would totally meld more CP onto the gear, just so that I could use this rotation, because that extra power coming from the Innovation is totally worth it. (and then 3x CS II would finish the item)
To be frank, I think you barely have enough CP to utilize Rath's rotation... as you can see from the above.
Like Silverbane said, before your final Byregot, your quality could be quite low, and it's OK as long as you have built up a strong IQ stack, and have saved up enough CP for a strong Byregot combo as ending. I still remember myself having the same question back in ARR 2.0: "But but but... I only have like 50% of the quality bar filled after all these puny touches!" And Sensei Nabeshin told me: "Don't worry if you have a strong IQ stack and saved up CP for a Byregot buffed under GS, Innov and Ingen2. The bar will fill to max in a single blow, and that's the magic of Byregot's Blessing!"
Thus, while manual crafting, I would strongly suggest you keeping an eye on the IQ stack as well as the CZ stack. You gotta juggle durab, CP, IQ stack and CZ stack all at the same time in order to determine when to use what. For instance, if you see that your IQ stack can only at most reach IQ8 before the Byregot, you might as well Reclaim... or you will have to somehow think of a way to increase the IQ stacks (like gambling it by adding an extra WN, but doing naked Hasty Touches without Steady Hand II, and then finish with a naked Byregot phase without SH). And for instance, if you have 2 CZ stacks left, but 30+ durab left, you can do 2x CS II to burn off the 2 CZ stacks, then renew CZ before moving onto the next stage of pumping Hasties. CS II "fillers" are very useful to help us get more CZ out.







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