So you're saying losing 1-2 Shreds is a DPS loss but opening with Berserk > Mangle (free) isn't a DPS loss? 90 energy is the ideal time to use berserk, without a CC proc, 80 with a CC proc. Otherwise you're wasting 20ish energy (maybe more but that'd be rng, half a shred basically). Additionally to make this all work, which again, is not ideal, you sacrifice 1.5 melees (1 second gcd coz using berserk before SR), which aren't buffed by SR. And the STS bite will be clutch anyway as it'll happen on the last-ish second of berserk. Additionally you're using only 2x 5 CP finishers instead of 3.
How exactly are you gonna sync your Rip and SR? They have different lengths and will get desynced in the cycle after that one most likely, especially as you will use SR with different CP. If you "desync" too often you're probably wasting energy on SRs (clipping it which would mean you made use of maybe 3 instead of the 4-5 CP you had spent on it), do it too many times and you've lost energy + CP for an extra bite (in the long run).
ICD watching is good, and will boost your DPS as you can afford (usually) to pool energy (similar with rogue, esp if trading tricks with another) and use the abilities with your procs.
The opener Gnimo and I have gone over is in theory the best, you can test however much you want but there's RNG in the game and the minimal DPS differences will not give you clear enough results.
TF before Berserk if you don't open with GOTW (forget or w/e). Can still do it even if you do but I prefer doing it after Berserk and you can go over my previous posts as to why (for whoever reads this)
And for the person above you, only skimmed through your post but rake over mangle will be a dps loss regardless of idol. Not just for you but for everyone in the raid.