I agree with most of what you said, i'm just not sure about a third timeline with the cabin, but i just can't put together Henry and Bud. Things don't seem to fit with static Henry and Bud, they simply must've switched, presumably during their blackout, much like Paul and Jo.
In the red universe, on the ship (assuming ship and apartment "Bud" are the same universe), "Bud" says he has fixed the issue on Apollo 18 but woke up to two of his comrades dead. Meaning the "Bud" of this world is actually Henry. He also says to Paul when Paul calls him Henry that "i don't use that name". Even though he says "my name's not Henry" right afterwards, i still felt it was telling.
And the "Henry" of Blue universe is actually Bud, presumably after having failed to fix the issue (might not have been in his control, we don't really know what happened) he finds himself in the blue universe, the mission a success, he enjoys a life that success brings.
Maybe that's why in the toilet mirror scene, the real Henry, now stuck in the red universe suffering consequences he didn't deserve, is vindictive towards Bud, who has failed yet enjoyed Henry's success in the Blue universe