From what I read you had an Adamas open in your pocket. It's a great knife (I love mine) but it isn't known for having a strong detent. You can look for folders with locks that put some pressure on the blade when closed (lockbacks, Tri-Ads) or something with a strong detent.
I understand your fears with fixed blades, but I think there's an easy way around it. I always carry a fixed blade on horseback, but since I ride on rough terrain (mountains) and train new horses as well, I've had a few traumatic encounters with the ground. I'd heard a few stories about riders injuring themselves with their knives, so I had a custom maker make me a nice sheepfoot knife (no point to punch through the sheath) and as an extra precaution I added an aluminium sheet to the back and tip of the sheath. Kind of what they did with the old pilot survival knives.
So in your case I'd recommend something like a Spyderco Enuff (H1 version is a serrated sheepfoot, should do great on rope) or Bark River TUSK. Get a nice reinforced kydex sheath and you should be good to go.