Sounds like the "sandy loam" wasn't all that sandy. At any rate, do not till it into the soil underneath or poke holes. If the mounds are melting, curb them with timbers or stones. Maybe after the heavy rains subside they will become less muddy. Truly coarse (sandy) soil piled onto heavier soil works great for providing better drainage for small plants.

And I'd say the sandy loam was TOO sandy :-) That much compaction after rain would indicate that the particle size of the sandy loam was too small and too uniform. Larger sized organic matter, like chunky compost, incorporated well into the loam should suffice. I too would advise against tilling into the existing soil - the tilling is not going to overly disturb the soil biota and you will be adding tons more with the compost anyway - tilling will further disrupt water percolation and could impede rather than improve drainage. Making raised beds, either hard sided or loose berms, of a good freely draining, organic based soil (like the compost mixed with your loam) should provide all the drainage you need.

Until all that compost decomposes and settles, leaving you with the original situation. Sand is the largest particle size below rock, more sand = more coarse. An excessively sandy soil is not going to make a "mud pie", anymore than it will remain in a ball when squeezed in the hand.

Mix some of your "mud" with water in a clear glass jar, leave it sitting undisturbed for a week to get a look at it. The components will separate out by particle size into zones as time goes by. Locally manufactured "soils" are often high in fine materials, I have done the jar test before and gotten alot of fine material.