no you cannot get proper compaction in wet conditions. proper compaction is achieved by having the correct moisture content in the dirt and then compacting in lifts with the right machine...
as far as using a skidster to get the muck out... you said you have 2 feet to get out in the basin and then its rock??? id take and ramp that skidster in there, ie - cut dirt away as you go in to build a nice shallow ramp....get down to the rock so your driving on the rock but scooping out the muck. you should be able todrive down in, get a scoop of muck and then back out with it....it is the same way we dig pools. the only questionable part is if you can get down below the muck and onto the rock without getting stuck.
