With enough wrestling I will get the stump out but my question is how much of the thick, immediate surrounding root stocks do I need to remove before I can plant a tree in its spot? Will the root matter of a young and carefully chosen specimen work its way around the decaying but well established roots of the old ash assuming I have freed an area only large enough for a new root ball to be planted?

Any advice is much appreciated, thank you.

Roots take years to decompose ecspecially the large tree roots. I've come across roots of an elm tree that was cut down 12 years ago...the Cherry tree just grew around it. In fact there was a major cherry tree root that grew under the elm root and then went back up.

you might also do to it what I do to every stump of mine: go to fungi.com and buy yourself 100 spawn plugs of your favorite mushrooms. Use 40-50 on the stump, the rest on whatever main root you can uncover. You can do it right away if you can protect the stump from the cold (with a pile of dead leaves) for the first winter only (I also cover every plug with wax, you can just melt a candle).
No need to protect injected roots if they are underground.

If you are in a hurry to decompose the thing (it will still take years before it is fully composted), oyster fungi are the most aggressive decomposers amongst the edibles, in fact they are first choice even for bioremediation of grounds soaked with petrochemical products. It always works if the stump is recent enough, and they do produce big flushes for many years once the whole root system is colonized (about two years).

The fungi idea just might be a good one...lemonade from lemons...

With regards to the oyster fungi- what is the best guess as to how many years of fungi induced decomposition before a significant portion of the stump is eaten up and we could replant?

AND while we are at it. Option C is to build a planter over the stump (everything else- deck, planters, water feature- are raised around it) and plant a new tree. Problem is said planter would be limited to 2.5' by 2.5' and the whole point is to get a tree large enough to help block out a the eye sore of an apartment building on the other side of the lane way. 10' away on the same axis is my 8' tall Acer Palmatum 'Bloodgood' so ideally we would plant a taller specimen that would not conflict in height with the Japanese maple. Any suggestions for a tall growing (15' or higher), limited root ball specimen? I believe a variety of Caragana might be good for this application but from what I know they tend to be a little dainty and wont provide the screening we are going for.

Thanks for the help!

acer negundo (my fav is winter lightning ), salix alba cericea, and heptacodium are all WICKED fast growers.
best,
mindy