Quickest way

I know its impossible to be run to HZH and Cavalon but I am wondering what is the absolute bare minimum of missions and quests to get there. This is my 4th char and I hate not getting the armor I really want until 3 missions from the end of PVE (which is what I do mostly)
Is it necessary to do all missions and primary quests or are there any shortcuts?

You have to complete Arborstone to get to House zu Heltzer and Boreas Seabed to get to Cavalon. Leave from where these missions drop you off and go through explorable areas to the opened doors of House and Cavalon. TBH, I haven't done this on the Kurzick side, but I have on the Luxon side, and I assume it is parallel.

I assume you want 1.5k armor. If you want 15k armor, you will have to complete the storyline through Gyala Hatchery for Luxon or Eternal Grove for Kurizick. There aren't shortcuts for 15k armor.

What about getting to Tanglewood (or in that turn Mattu Keep cause i know i can get from there on) are there any missions that MUST be done to get there...I cant remember if I have to do a mission to get to undercity....