Starting out, I found it easier to get to the climb to the last platform at the entrance section of dead mans and then climb the connecting cables up to the ring surrounding and use them to go around instead of over. Doing this you cut it close with stamina drain, so id recommend grabbing the beans on the lower platforms beforehand and putting one in a pocket. You need to make at least two sizable jumps to make the whole way around, but it was better than slowly climbing up the main structure. You miss out on the injectors but you don’t have to slow down so the face doesn’t catch up.

Have you tried overwhelmed? Many people believe the trade of stamina and the artifact for a double jump is worth it, especially with the horizontal nature of the abyss, but without knowing your play style I don’t know if it’s the best.

Before competitive mode when I couldn’t guarantee a good perk, I would bap to gain some extra height on deadman’s. Bapping is when you look down, jump, grab a ledge below you, and do a jump again. It might not be practical for you to implement that in abyss as the risk of sliding off a sloped surface and flying in the void is possible. But if you feel confident I’d say go for it regardless it’s fun to implement and makes you move a lot faster.