Here are some advices I learnt after doing PoH (and dieing) several times:
How to blitz through 4th, 6th and 7th floors when portals are open and mobs respawned:
Floor 4:
there is only one cultist hidden right before portal room. Sometimes I found it right inside portal room. You can usually run past it without being spotted: just run, don't stop, don't jump, when passing thru the grate door (where cultist hides behind) hugh the left side of door.
If you get aggro, don't worry: just jump on the libraries placed into portal room, this is usually enough to make cultist run out of the room, then you are free to use portal.
Floor 6:
in the two large squared rooms there are altairs on the right side: use them to lose aggro. Caution: they seem to work for one toon at a time only, so if someone is already standing there, don't use it.
Next room north is a small square room with 4 firelights: you can jump on firelights to lose aggro, especially when dealing with the cultist elder standing 2 rooms forward.
Let her spot you without rushing toward her, so she won't spawn her pet, and will start chasing you instead. As soon as she starts running, go into the firelights room and jump onto one of them.
Cultist elder will run away southward, then you are free to run up north.
Caution: her pet will ignore all firelights or altairs and will kill you anywhere, that's why she should not have the chance to spawn it.
To deal with horrors sitting near (1) and into (2) portal room, best way is still to run fast trying to target portal in advance and use E as soon as you are in range, again don't jump, don't stop, and maybe they won't spot you.
If you get aggro, just run down and jump on a firelight to lose it.
Caution: horrors won't see you if you are on a light before it enters the firelights room.
If you jump when horror already is into that room, it usually kills you onto the light.
Some ppl can just do a single run from start to portal without aggroing any mob. I guess fixer speed or Rage may be helpful.
Floor 7:
As soon as you click on Floor 6 portal, you find yourself into a room with a couple mobs. Just run through doors and follow the path ignoring all mobs until you reach Maiden's arena: as soon as you enter it, jump on the small altair at the right side and you'll be safe.
Pyramid of Home Guide (Patch 18.8.6) - please contribute!
Re: Pyramid of Home Guide (Patch 18.8.6) - please contribute!
Thanks, looks like a nice addition, Agamundos 

Re: Pyramid of Home Guide (Patch 18.8.6) - please contribute!
updated team recommendations, significantly updated tactics on Phobettor, added basic and advanced tactics on phobettor, added more detailed tactics on Ajada the joyous.
" I Don't Like That Man. I Must Get To Know Him Better." -Abraham Lincoln
Re: Pyramid of Home Guide (Patch 18.8.6) - please contribute!
Mach upgrade Sigil of Bahomet to Sigil of Samael
¯\_(ツ)_/¯