Sticky clay requires the addition of calcium (and magnesium to a lesser degree) to cause flocculation of clay particles and contribute to the crumb-like texture which is the hallmark of good soil with good drainage.
Compost, while a good (eventual) source of humus, is not a significant source of minerals. Quoting from: http://www.soilminerals.com/compost_manure_humus.htm
Let's look at another factor in using compost or organic matter as a mineral source: How much would we need to use to add significant amounts of needed minerals to the soil? This gets a little difficult to quantify, but going back to research done by Davidson and LeClerc in the 1930s, we find that the amount of Potassium found in ash from commercial vegetables was around 7%, the amount of Calcium averaged about 2% (they also measured 95%+ moisture content and 20% ash from dry matter, which leaves only 1% total ash, but let's be generous and stick with that 1 1/4 lbs we came up with above).
1 1/4 lbs= 566 grams
566 grams x 2%= 11.3 grams Calcium per 100 lbs compost
566 grams x 7%= 39.6 grams Potassium per 100 lbs compost
Even a sandy loam requires at least 2,000 lbs of Calcium per acre for best growth. What if we measured the minerals and found that we needed to add 1,000 lbs of Calcium? How much compost would that take, at 11 grams per 100 lbs? I'll spare you the arithmetic: It would take about 4,000,000 lbs: Four million pounds of that 75% moisture content compost per acre to add 1,000 lbs of Calcium. Wait, it gets worse: While we were adding that 1,000 lbs of Calcium we were also adding almost 4,000 lbs of Potassium, far too much. Well balanced soils need about 1/7th as much Potassium as Calcium, so this soil would call for about 280 lbs of Potassium per acre; we would be adding over 3,700 lbs too much, assuming that we were crazy enough to try adding four million pounds of compost anyway.
Putting that in terms a backyard gardener could relate to, one would need 90,000 lbs of compost per 1,000 square feet of garden just to bring the Calcium level up to par.
Concerning how to add organic matter to soil, I would favor grass clippings to anything else.
1) Its easy to find in large quantities, like leaves.
2) Grass is green, therefore having chlorophyll, which is a compound containing 4 nitrogens around a magnesium.
3) Grass has proteins which also contain nitrogen.
Dr. William Albrecht explained why nitrogen is important in organic matter: http://www.soilandhealth.org/01aglibrary/010120albrecht.usdayrbk/lsom.html
Thus when decay has proceeded to the point where the carbon-nitrogen ratio is significantly decreased, a residue of a more stable nature is produced. Thereafter the carbon-nitrogen ratio is narrower and remains more constant. This corresponds more nearly to the condition that holds in the case of the organic matter in virgin soils. Its further decay, which is slow because of the relatively low level of carbon, liberates nitrogen in place of storing or preserving it. Because of its high carbon content, the decomposition of fresh organic matter requires additional soluble nitrogen to be used as building material by the micro-organisms, which obtain it from the soil, often exhausting the supply to a degree that is damaging to a growing crop. The amount of increase in organic material corresponds, in the main, to the amount of nitrogen available. The extra carbon in the fresh material is lost from the soil. Thus when soils are given straws, fodders, and similar crop residues of low nitrogen content, only small increases in soil organic matter can result--in the main, only as large as the added nitrogen will permit. Many tons of common farm residues and wastes per acre are needed to produce a single additional ton of organic matter in the soil.
The restoration of soil organic matter, then, is a problem of increasing the nitrogen level or of using nitrogen as a means of holding the carbon and other materials. This is the basic principle behind the use of legumes as green manures. In building up the organic content of the soil itself, it will often be desirable to use legumes and grasses rather than to add organic matter, such as straw and compost, directly. If legumes and grasses are to be successfully grown on many of the soils of the humid regions of this country it will be necessary, first, to properly fertilize and lime the soil. Legumes use nitrogen from the air instead of the soil, and thus serve to increase the amount in the soil when their own remains are added to it. Commercial nitrogen used as treatment on straw for the production of artificial manure in compost piles, or when plowing under straw in the field after the combine, may be considered in the same category. Small amounts of added nitrogen may in this way make possible the use of large amounts of carbonaceous matter in restoring the soil.
So the remedy for hard clay would be lime and grass. You could apply the lime, then a thick layer of grass clippings, then apply your bagged soil over the grass clippings to trap the nitrogen in the grass from escaping as ammonia into the atmosphere, then apply more lime (unless bagged soil is already high in calcium) and nitrogen fertilizer. The result would be fairly healthy soil, with no digging. This is how I renovated my lawn. For the garden, I alternate layers of grass and soil.
I would cite more references, but for reasons I can't imagine, I am not allowed.