Been playing since November. GW does indeed seem impossible at times but I have been able to clear it regularly. Here is my attempt to help others be more successful.
There was a previous guy that broke down characters I think that information is still relevant.
My main team is Phasma (lead), Sid, Lumi, Poe and Kylo.
I have a fairly deep bench (I will get more into this).
For the GW nothing seems more valuable then the extra attacks Phasma provides.
Others choose healer leads but I think this is counterproductive. Often times you would be much more effective with a character that can do more damage. Phasma's assist can bonus and allow a final blow taking out a character and any potential damage they can inflict. Even Sid or other critical effect leaders are more effective.
Targeting priority should always be to Dakka. I don't have her yet but I am sure she would be a useful addition to a GW team.
Glass cannons can be dealt with second if they have not had a chance to execute their specials (FOTP and Lea are exceptions, deal with them after Dakka). If they have not executed specials and you can kill them prior to execution then they should be targeted first.
If not target healing blockers. For example, once GS or QGJ has assisted attack they are not big threats for a couple turns.
Your next targeting priority should be any character that inflicts a healing block. Sid, Kylo are the main two I encounter.
Of all the healers Lumi should be targeted first. Her heal gives healing over time and she hits harder than most.
When dealing with healers and tanks last you can delay the game by spreading damage and allowing the opponent healers to heal. This allows you and flexibility and time to deal with your cooldowns.
When you encounter a team that is much stronger there are two alternate teams that you can use.
The first is a mid level team that has the ability to inflict damage or possibly take out a single opponent.
The second is a team of level 1 to level 10 characters. This can often be effective enough to elicit Phasma's VM, Sids AOE, Lumis FA, etc.
As many have noticed no matter how many times you repeat a round the outcome is always the same. Specials hit, targets don't change etc. allowing a suicide squad to run will change the possible outcome. Even if it is only a single lvl 1 toon.
If you're not beating the GW each day you should evaluate where you are dedicating your resources. A well geared level 65 team can inflict serious damage if not beat a level 70 roadblock team with significant casualties.
The difference between level 65 in level 70 may not be enough to dedicate the resources needed to those last five levels.
However having a multitude of level 65 characters to throw at roadblocks will.
Hopefully that helps.