I haven't dealt with that particular soil type, <sounds like some sort of chalk, perhaps?>, but I can give you a couple tips for long term improvement.
1. Keep planting in your mushroom compost and leaf and hay mulch for now, that was an excellent idea. You can use any or all of the three in conjunction with the following.
2. If you can deal with the labor, dig a hole, put in a layer of fresh garden compost, then layer in dirt>compost>dirt until hole is filled. Dry stuff like leaves or end of the season garden detritus can be layered in also. This usually is only two compost layers deep. Layering in the dirt does two things: it adds the soil microorganisms more directly to the compost, and puts the decomposing material where it'll be worked into the soil sandwich more thoroughly and quickly. You'll want at least two or three inches of dirt as the top layer to keep the smell from escaping.
3. If you don't have the time or
energy for all that, just scrape back the dirt, add a thick layer of leaves, put the dirt back. you can put a thin layer of compost underneath or manure on top of the leaves if you are worried about nutrition levels. This does two things: gives you a non-burning, non-compacted layer of moisture retention right at root level, and gives you an instant
raised bed effect. You only need about an inch or two of dirt to top this.
I use both of these. Neither magically improves the soil overnight, but over a few years it makes a big impact. I try not to plant over fresh compost, so the compost holes are rotating and we try to get them done in fall or the mild part of winter for the areas that are going to see the most use. The raised leaf bed can be planted immediately after making it, and I've had lovely results, the only downside is that it needs more manure or other fertilizer such as fish emulsion during the growing season for heavy feeders, since leaves are a bit low nutrition. But squash will grow like crazy on it with no extra effort.
Edit: Tilling is a long standing farming technique, but over time it damages your soil, letting nutrients escape, breaking down the overall tilth of the soil, and creating more run off and more loose soil that blows away. Particularly with fragile soil types. It you feel it is something that is integral to your garden, you might want to make sure you have a heavy layer of mulch [rotten hay springs to mind], to till in when you till, which should at least help the tilth of the soil.