I had the same problem since my tiny twister also had more HP than the crazy carrot. I used Zephyrian Prince, which has the same two required abilities but less HP than crazy carrot. With that substitution, I 1-shot Gloam with this strat.
Just came up with a strategy after going through around 100 bandages and 2 hours of my life. I'm unsure if it works every time as I was constantly tweaking strategies with spells and pet combinations and some how this one worked on the first attempt.
Please note that if Gloamwing crits at ANY time during the fight you will have to start over.
1. Pass (Amalgam of Destruction is swapped in)
3. Cataclysm (If Gloamwing kills you here, restart) (If Cataclysm misses, restart)
4. Pass (Corrupted Blood is swapped in) (You may end up with a stun here, but do not deviate from the strategy as you will need to cast Explosion before the next swap or your toast)
5. Scorched Earth (Same as above regarding stun)
6. Explosion (Corrupted blood dies)
7. Fist of the Forest
8. Lash (Depending on extra damage per round from Scorched Earth will determine if you need 2-3 lashes)
I ran this pet combo probably 60 of my 100 or so attempts with different spell combinations and with good RNG would get Gloamwing between 31-151 HP.
Hopefully this can help some of you if you were still looking for a strategy besides the ones listed above!