Thanks a lot for the great comments!
I forgot to mention that the PC's are level 7, so they can take some beating. And beaten they will be (since I know what awaits on the top ...)

It's homebrew, but long story short do they have to get to the top, pass some (undead?) guards and go through an undead, but 'sleeping' army waiting for commands. The aim is to destroy a powerful artifact, that otherwise will give great advantage to the undead army in the looming war between the living and the dead. Not unlike GoT, though this has a wastly more complicated plot behind, that the players will have another 2 campaigns to unfold and stop.
The platforms are 5-15 feet in size. The rope is long enough to provide 30 feet between the PC's (so it's likely some 50-60 feet in total).
One player has levitate but sadly isn't joining this session. Another has Misty Step, which I'd say makes him leave the rope behind and otherwise work as usual.
I have decided to go with quite a few suggestions, so the rules will be:
- No falling to their death during climb though I might use say 2 rounds of rolls where a 1 mean that the falls should be of 1d4x10ft for 1d6s for each 10 feet fallen if hitting a ledge, half if caught by rope and hitting the mountain side, just to keep them on their toes.
- If falling more than 10 feet: I will roll for equipment lost (will create a small table). Concentration is broken on all ongoing spells.
- Strength check to prevent next PC from falling after the first one if tied together. The guides (mountain dwarf) need no check.
- No punishment for the plate armor aside from being shiny and noisy.
- Jumping to a platform in same level: DC10 DEX (acrobatics) save for a good landing. If failed roll another DC10 DEX (acrobatics) save to fall prone instead of falling to the next ledge. If/when landing on a shelf during a fall roll DEX check (15) to not fall further, advantage if tied to an ally.
-Jumping up is according to RAW; 3 + STR mod if 10 feet movement first, half if standing. If arms are used to heave oneself up can 1½ the persons height be added
(my addition: if empty handed, otherwise only additional 5 feet).
- No 1d20 rolls for walking on ledges but instead the suggested Athletics/Acrobatics check DC 10 IF the character moves faster than 1/2 speed. No check needed for goblins or dwarves.
- Concentration/Athletics/Acrobatics checks if a character gets hit while climbing (both PCs and NPCs).
- Attacking while climbing or while holding/being pulled by the rope of a fallen ally has disadvantage.
- The goblins will have a few traps in place.
Oh, and I hope to get to throw in Bill Zebub's "Touching the Void" option. I'm sure it will make for interesting conversations around the campfire later on
I'll let you know how it went in a few days. Once again, thank you SO much for your input!
