none of the chemical methods that would work would be either safe nor cheap. Not to mention soil contamination
if you can burn it out, that definitely works - be aware the fire will burn for about 3 days underground and follow the roots. suitable for the countryside in winter, but less so for suburban housing.
cutting digging and manually removing the stump is probably the cheapest option if your labour is free. high pressure water helps a lot if there is drainage, or a sump pump.
explosives work... but are also not cheap, and not suitable for an urban environment.
WRT aggregate - you really want angular rock for interlocking and stability. Consider recycled brick - cheaper than road agg, has similar properties.
without knowing the specifics of the problem, I can't advise better.