Hades gate with cooldown could work under one condition - really high wdm so it deals massive poison damage via wots, I mean comparable to snake stance stampede levels. -poison resist synergy would be another way to do it, if skill like that is possible.
I remember back in the day where hades gate + broadside switch nagi build was a thing that was main reason it worked, but it was not to high hades gate multipler, but just simply wots was overtuned as hell, and it was dealing more damage than snake+eagle (60points).
It would be probably better to have flat cooldown on hades gate but really high like 150% WDM mod, so that poison really stings. But at same time because of cooldown it wouldn't really benifit from high naginata damage or other ways, since you hit with it once per few seconds. There is that hades gate proc that should be taken into consideration with such change of course. One factor that "balances" it is that it teleports you randomly which can kill you in place like duncraig or straight up slow you down if it teleports you back in area you already killed everything.
As for broadside, I think it can work ok, but as it always did early game with it sucks with massive cooldown.
Very lategame pure broadside with 6s capped cd and full xis setup insane gear it is still not that impressive, kinda slow kill speed in p1 duncraig, but I think it comes down to lowish damage from wotp and wotg, because mechanically skill is the same as it used to be, and it used to melt things really hard.
I think for the endgame cooldown could go bit lower too, 5s wouldn't break the game and make it little more viable.