Jay, I agree that supplementing the nutrients in compost is very important.
One factor is that most of the nutrients in compost are not plant-available in that form. Nitrogen is mostly bound up in the proteins that make up the organic matter in the compost (P, K and micronutrients as well). The compost must go through biologic decomposition in order to release (or mineralize) the nutrients. For that biologic transformation to occur, you have to add enough nitrogen to make the carbon:nitrogen ratio (C:N) equal to 23; more nitrogen is better. Chicken poo, or nitrogen fertilizer, will both do the trick!
Another factor to improving the soil is to till when the soil is relatively dry. Certainly not when saturated. Try to minimize compaction with equipment when the soil is wet. This preserves soil tilth and structure. Ideal soil tilth is indicated when the soil is friable, breaking into small to medium aggregates. Neither powdery, nor breaking into large hardened clods. The best tilth comes in the ideal 'loam' soil texture, which has roughly equal amounts of sand, silt, and clay (those roughly equal proportions are the definition of a loam soil). Adding in the organic matter will also improve soil structure.