I think most groups get to this point and ultimately most just throttle DPS, which isn't necessarily a bad thing, the enrage stays easy and unless you guys want a good clear time or good parses it's not too important.
If you DO want to push it, there are basically a few timings which vary in difficulty/shittiness
1. Pushing RIGHT after Rage. Terrible, I don't recommend this, Gigaflare + wyvern at the same time, the level of healing required to heal up the group after Rage going into Gigaflare, and then Gigaflare into Dive Bombs, while maintaining aggro, probably requires Shroud and a little luck.
2. Pushing right before Rage. The window for this is actually huge, basically if you get the Megaflare before the 2nd Rage it's within that window. It can be pretty hard but do-able, Dive Bombs are a pain to fight wyvern with efficiently and have all 8 members dodge, and you might need Cover on the WHM depending on if the wyvern spawned after AoE healing or not. This timing is annoying though, as I mentioned before you should only take this timing if you're just looking for good records/numbers, throttling for 20s is usually better than risking a 4m~ run on this situation.
3. Push before Megaflare. This is the goal if pushing wyvern, and the earlier you push the better! If you push early enough, wyvern spawns as the adds spawn, have one tank take the wyvern, one tank take both the other adds. You may have adds up while the Sins spawn but if you have enough DPS to get this push timing you have enough to kill everything before the Sin's eyes. If you push before Megaflare but RIGHT before Megaflare, the wyvern will spawn during dive bomb Megaflare of sorts, it's not necessarily hard but don't let your tanks get caught off guard.
It's easy with the 3rd timing, but I'd probably recommend most groups stick with throttling TBH.
