Stump removal options?

There's a stump in our front garden with a gap of just over a a border spade width between the stump mass and the wall over the pavement. The only access to there is up narrow stairs and across the lawn. The stump is coming out of a large mass of wood. We're talking a foot diameter stump above nearly a metre wide mass. From this there's huge roots almost as big as the stump, we've cut through a few smaller roots up to about 3 inches but there's at least 5 very large roots that we can see after digging down around the stump mass. Although we haven't dug deep enough to be sure those 5 roots are not more, solid mass too.

So that's the problem. What's the solution?

We've tried digging and cutting roots out like we did with other tree almost as big but that had no big mass like this one. It came out after a relatively easy bit of grunt work.

We've contacted quite a few tree surgeons round this way that had the good qualifications and reputations. Not one was able to drop round to inspect and quote even though we have two stumps, a tree and need all the other trees checked out too. Too small to bother with? They certainly seem to be busy right now.

I've seen stump grinders, they have two wheels to support the weight and you tilt the grinding wheel up and down to take the stump away. Not sure we could get one up the stairs if we hired one.

At the moment we're using a mattock, spade, trowel, bow saw, folding pruning saw, small hand hatchet and a felling axe to clear a root then cut or chop it through. We've done two big roots about 3 or 4 inches diameter and maybe 6 small ones up to an inch and a half. The really big roots we haven't got to yet. It's hard work and doesn't seem to show any progress for all the graft.

We were wondering if there's a more mechanical solution. Perhaps take a type of chainsaw to the roots or stump mass? Or a mechanical saw of some other kind?

What's the best advice of the collective?