My own speculation is that there is no Rapid Fire in use here, however, double weaving remains a necessity depending on what Wildfire and 'Not Overheat' entail.

In 8 seconds, at base speed, that should be a Cooldown at 7.5, 5.0, 2.5, so with increased speed that'll be 7.5, 5.X, 2-3.X, and 0.X for four total GCDs.

Tools seem to be OGCD, so we know that Gauss, Richochet, Auto Crossbow, and Giga Drill Breaker are here. It is unclear if it would be worth attempting to do Bio/Flame in the Not Overheat window, as well as whether we retain Heartbreaker or gain other OGCDs not shown.

And while it is not currently a thing, it is unknown if Gurenn Lagann contributes to Wildfire. For the sake of a "Worst Clunk Scenario" lets say it is, but independent of Overheat.

It is currently not known if Wildfire and 'Overheat' will line up as they do currently, but we can assume that with the resource stocking, that you will always have overheat for Wildfire. The better question is how the Tools line up with Wildfire.

We also do not know Cooldown's relation to the other shots in terms of potency, or if Cooldown even just straight up replaces those shots. We will work off the assumption that cooldown replaces other shots.

A wildfire window would thus look something like...

Summon Gurenn Lagann up to 10s prior.
Finish off current Shot Combo.
During the OGCD - Wildfire + Overheat
Cooldown 1
Tell Gurenn Lagann to Giga Drill Break
Cooldown 2
two of the four OGCDs
Cooldown 3
Two of the four OGCDs
Cooldown 4
Overheat ends. Trigger Wildfire (or let it expire if trigger is unnecessary)

I want to be optimistic and say they've probably considered this scenario is still unfriendly to latency spikes, but that is worst case.