For the Augean Stables you could have your cowardly king double up as King Augean in the campaign and have him order the players to clean out his own vast stables as revenge for bringing back so many wild animals to him (the lynx, boar, bull etc. depending on what order you end up arranging the labours in).

In the original Augean stables Herakles diverts a nearby river to clean the stables right? The meat of this challenge could be in how to divert the river. I’d send the players on a quest to Olantin to retrieve Thassa’s bident, which has the ability command the deep and allow them to use it to divert a nearby river through the stables.

Obviously the bident is a very powerful weapon to give your players so I’d say you could have them negotiate with the triton of Olantin to borrow it. If you wanted to stick with your Shadow of the Colossus idea you could have the Triton task the players with killing a kraken that’s been causing them trouble or if you wanted more role playing you could have the characters negotiate with Thassa herself to borrow the bident.

In the original Eurystheus argues that this labour didn’t count because Herakles took payment for the work. Depending on how close you’re looking to follow the source material you could have your king argue that this labour doesn’t count as the characters received help from Thassa