sounds like a lift, clean and place oppty in any and all situations.
I suck at golf and still after 3 years trying to figure it out, but if it's played like a fairway bunker, for me i don't play all fairway bunkers back in my stance when i just need to get it up higher to clear the lip. I'll put it more forward in my stance and hit a higher lofted club but try and hit it clean so I will choke up and obviously not rest my club on the sand.
As far as hitting off of mud, if it's recreational golf, just lift clean and place it. If the bunkers are also muddy in low spots, my group might say play it out of the bunker. No sense in having a no-fun golf round to pretend you are on the PGA tour, which btw they get to play off much better courses than we all do.