There's an issue with this idea. Yes, the bird becomes hungry every 15 seconds if we don't feed it a worm but we only have 4 worms each to counteract tantrums/hungry. Obviously, it's a good idea to use all of the worms because, not only are they annoying to the rest of the raid, but the more uptime on satiated the better.
If we were to have the bird eat a worm every 15 seconds in order to make sure that we have minimal hungry time, that would only give us 1 minute to kill the bird which, since the bird has ~30mil. hp, calculates to 500k dps overall to the bird. Obviously this isn't possible and phase 1 lasts longer than a minute so, while what you said is correct, it's a better idea to use the worms *reactively* as opposed to proactively.
If you have a bird eat a worm while it is in a tantrum, the tantrum goes away. So, what I usually do (and this was merely a matter of feeling out how it all works through trial and error) is eat the first tantrum, then feed a worm during the 2nd tantrum. From then on out, I have the bird eat a worm whenever it drops below a 20% threshold (80%, 60%, 40%, 20%) if it has not already gone through a tantrum or reactively when the bird throws a tantrum.
I'm pretty sure you already knew most of this and, even if you didn't, you have a system that works anyway (we were reliably getting into phase 2 although a lack of worms may have been why you were dying alot as we transitioned into phase 2? maybe? I don't know).
tl;dr: I don't know why I wrote this because you already know what you're doing here.................. fun times.
Does it spawn hungry? If not, we got 15 seconds at the start before first worm then we also got 15 seconds at the end. Don't forget the "Lock on and fire" animations when the hatchling is moving towards and eating the worm. So think of it like:
0 Seconds - Spawn
15 Seconds - Hungry. Dragged to worm
17 Seconds - Starts eating worm
22 Seconds - First worm eaten, back to tank
37 Seconds - Hungry. Dragged to worm
39 Seconds - Starts eating worm
44 Seconds - First worm eaten, back to tank
59 Seconds - Hungry. Dragged to worm
61 Seconds - Starts eating worm
66 Seconds - First worm eaten, back to tank
81 Seconds - Hungry. Dragged to worm
83 Seconds - Starts eating worm
87 Seconds - First worm eaten, back to tank
102 Seconds - Hungry. Tornadoes spawn by then?
If we need a bit more time, we can always shield wall the first Tantrum. I'd imagine it'd be up by the time phase 4 happens.
Also, while what Prydain said was indeed hilarious, it brings up the following thought: If we do the adds perfectly, we're losing vengeance stacks from the few tantrum hits that do go through and that will affect our DPS. I'm wondering if we should just keep doing what we're doing instead. At least on my side, I do it somewhat sloppy and just bring him to a worm once he tantrums so I take a few hits (I'm always right next to the next worm.