All of the soils east of the Mississippi River tend to be acidic, because of the normal amounts of rainfall we get, but whether you wood ash would really be of any help depends on many things that only a good, reliable soil test can give some direction for. To speed up the digestion of the tree stump add a source of Nitrogen that will feed the bacteria that do the digesting. What else to do depends on what that soil test and knowing more about your soil tells you.
What is the level of organic matter in that soil?
What type of soil do you have? Sand? Clay? Loam? Gravel?
What is the level of life in that soil?
How well does that soil drain?
What is the tilth of that soil?
These simple soil tests can help answer those questions,
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer you soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

Here is a link that might be useful: NCSU CES

If I had a rotting stump, I would try to plant mushrooms in it.

Here is a link that might be useful: mushroom

To speed the process of rotting the stump, you'll want to add Nitrogen and Potassium. Urine has both. I'd keep the stump damp and covered with organic material.