You are forgetting the 20% healing taken increase from SW. As a person that used SW a lot this expansion (read as: T14), I can say it is extremely underrated. Taking 20% increased healing when you already have 20% healing done increases the healing from you SoI by 44% and your EF (which we will probably see on a few fights) by 44% aswell.
I dont know how my guild would have done Elegon Heroic without me using SW to be honest, well of course we would have done it, but would have been a lot more wipes. The amount of mana it saved for the healers and the help it provided in the burn phase. I could tank the entire burn phase without any external heals thanks to SW. It just works so insanely well on any fight where a tank can heal himself a lot.
Also, you are looking at the raw throughput.
The napkin math that I did earlier showed the presuming you are starting from 5 HoPo and J + CS off coldown (i.e. you know a damage heavy phase is inc and you prepared for it)
50% haste
Not counting GC procs HA SotR wall lasts for 51 seconds and SW 57 seconds. 57 second sotr + 20% healing taken > 54 second SotR. Should be noted that the HA is 54 seconds~ since after 51 seconds it is only down for 1 second before you get another 3 seconds, so maybe fairer to say 54 second for HA, even though it techincally drops after 51 seconds.
Even if you get say 2 GC procs during the first 18 seconds (HA) it would result in a 66 second HA wall 63 second SW wall (with 20% healing taken).
So you would need to get atleast 2 GC procs for HA to pull ahead in SotR uptime. But in my opinion that healing taken increase bet the heck out of the difference between a 63 or 66 seconds SotR. It is not even a competetion in my eyes.
If you are getting more than 2 GC procs during HA, it is likely that you can abuse GC on that fight, why are you even considering HA or SW then? GC abuse fights = DP. The only time that really HA is gonna be viable in the next tier is if you need a cooldown exactly every 2 minutes. Which becomes kinda mute as soon as you got the trinket.