Steve, how deep and soft is the mud? A folkboat would only need to sink down a foot or so into the mud and it would be on its garboards and stable enough to sit upright or just heel a little.
Depending on the mud, your moderate long keel may prove to be an advantage.
I have been fooling around on the edge of a soft muddy tidal creek for nigh on fifty years, with fin keel, round-bilge centreboarder, moderate long keel, and flat bottom (no keel at all). In deep mud, the fin keeler sat bolt upright. The round-bilge centreboarder was hopeless on the edge of the creek, heeling alarmingly and acceptable only on level mud out of reach in the middle of the creek. The moderate long keel (in which I currently live) sits up very well on sloping mud at the side of the creek and with a little training has dug a hole for itself into which it obediently returns with each tide. The flat bottom scow, which I thought would be ideal, is not really ideal in the creek. However it is tied to the bank, it always insisted on slithering down the slope and taking up residence in the centre of the creek and would never learn to stay close to one side. (It sits up perfectly on a level mud bank, of course.)
I have often wondered about the use of legs, for sitting up on firm ground - but legs are not commonly used here and I don't have any experience of them.
I agree with Annie and can't see the mast ever being a problem in any case.