I amend my own opener slightly to avoid this Hot Shot/GR situation. Weaponskills after Wildfire detonates notated as a/b/c/d, since you won't have ammo for those and will have to choose them accordingly as needed.
hot / pot
lead / reload
split / wildfire
slug / gauss round, reassemble
clean / quick reload, rapid fire
split / ricochet
slug / head graze
split / blank
clean /
slug / (Wildfire goes off here)
a /
b / quick reload
c / gauss round
d /
hot#2 /
lead#2 /
For me, that position of Gauss Round is the only position in the typical opener that avoids it coming back off cooldown at an awkward timing.
It's not possible to fire it the second time any earlier (since the first use of it is already as early as possible). And if you put it any later in the sequence, it will come back off cooldown at an unfavourable timing as you can see.
The ogcd slot after d is risky because it's extremely close to Hot Shot's buff dropping off, if you lag a little you run the risk of the buff falling off just as you fire it. The ogcd slot after the Hot Shot refresh is likewise unfavourable for the reasons you mentioned. So there's basically a 2-3 second chunk of time over there I want to avoid firing Gauss Round in.
You could also go the other way to avoid it, by rearranging your ogcds during the opener so you fire Gauss Round later, so that by the time it's available again that Hot Shot refresh period has already passed - but that's more troublesome if you ask me. If you swap its position with Quick Reload or Ricochet it will come up again during those 2 unfavourable GCDs. You would have to move it at least 3 GCDs down which is more than I'm comfortable with. Since Gauss Round has a short cooldown (20s), I prefer to use it earlier and hope I can an extra use of it later, since you are starting and cycling through its cooldown earlier.
Side note: you don't want Quick Reload coming back on the d and Hot#2 GCDs either for obvious reasons, since ideally you 1. want to use it on cooldown, but 2. don't want to spend ammo on Hot Shot and Lead Shot.