If you were prepared to provide a more permanent solution for the wet ground, a trailer of 4" down would make a nice sized area for interaction feeding. Delivered by a tractor with a dump trailer they will be able to let it out whilst driving off which spreads it nicely into a drive 12" thick on top of the mud, then hire a vibrating plate for a few hours and give it a whack.
the stone will likely be around £10 per ton but it wounld be £100-150 very well spent.