Unless there is time pressure, this is hard to make interesting. Some tension factors -
- Each success moves the characters higher up, making failure successively more catastrophic... though I guess anything above about 120' could be deadly.
- 550'/30 = 18 so potentially there are 18 checks here... no one is going to make (1-DC)^18 checks successfully...
- You've hinted there are checks characters can make to help their chances. Each such check should take a turn to make. Such as a turn taken to place a stay or anchor.
Okay, suppose characters sensibly rope themselves together and/or use anchor points to limit their maximum fall. The wall takes 18 climbs and there are three numbers to consider.
- Wall DC (say 10 for the first 6 climbs, 15 for the second 6, and 20 for the last 6). This is the chance of no progress for a character. It gets harder as higher for, you know, tension.
- Wall DC -5 (5, 10, 15). This is the chance of a fall using the DMG guideline for a catastrophe.
- If there is a fall, you need to know how hard it is to stop, and what can stop it. One option is stays or anchors. Those might be made with Intelligence (Sleight of Hand) as recommended in Xanathar's for Tying Knots. It's up the characters how many stays they set. Another is they might rope themselves together, in which case it would be something like a Strength (Athletics) to stop a fall with a catastrophe being to also fall. Or both. Perhaps it is simply 5/10' fallen + 5 per extra character falling? So if a character has a stay or a character they are roped to 20' below them, they are saved on a DC 10. The stay breaks or the other character falls on a DC 5. I think for simplicity I would not use the -5 guide here, but just a succeed or fail... with fail meaning plunging to death. Or you do, meaning a simple fail is their fall continues but is effectively restarted at the height of the stay, while only a fail by 5 means they plunge to death?
Anyway... this doesn't really come to life unless there is a time and/or resource pressure so that they can't just set a million anchors. How much rope do they have? How many turns do they have? Imagine they had 60 turns, then they could fix a stay every 30' (18 turns) allowing them to make no progress on 24 separate turns of climbing (two characters making no progress on the same turn is the same as one).
I think something like this - generous chances to not fall and backstops to be caught if falling - while keeping the danger absolute: if there is a cascade of calamities you are dead. Could work. It's a lot of checks to make, but should be quick if you just get everyone to roll for each turn simultaneously, and get them to declare stays, but not roll for them unless they are needed. You'll need a way to keep track of progress. If they come up with something clever then that can be incorporated as a reduced DC or extra save.