How to clear outbound blockage using the snake/auger?
I can't see to the back of the fitting would it be possible to cut the pipe and use a coupler or union to repair when done? Each 90 causes a large amount of force to be required, with a 90 at the start then probably another 90 in a few inches that will make it tough now go down to ground level and another 90 some may be sweeps or t's but the force still jumps with each one.  Next are you spinning clock wise? You want the augger to pull into the plug turning counter clockwise actually pulls the snake out while you are pushing. Plugs can be tough to work through with a small snake but if you are pulling stuff back up you are getting close , I have power snakes and have had to hit a plug 20-30 times where other times 1 times clears the plug. If totally stuck look for another entrance to try, the roof vents are usually a good place but may require a longer snake. Some homes have a main back bone with a plug at the washing machine in the garage so there may be other ways to tackle this but if nothing else in backing up I would keep trying.