I highly doubt you will have much luck inoculating shiitake on to a stump. Shiitake mycelium runs very slowly and it is more likely that some other type of fungi blowing in on the breeze will beat it out and colonize the stump. It is especially tough inoculating aspens, since they rot so fast, 9 times out of 10 you will get some kind of crust mold or other undesirable type of fungi winning over shiitake.
I would suggest you look into oyster mushrooms. They are the fastest running of all cultivated mushrooms and generally will produce much more per log than any other species. You will also get many more flushes per season.
Lion's manes are a wonderful mushroom, but again the mycelium is rather slow. I don't know what type of tree the cultivated verities are
native to, but here in Michigan we have a type of Hericium(Hericium coralloides) that grows on aspen and birches. Also there is a type of oyster (Pleurotus populinus) that produces prolifically on dead aspens.
It is unlikely you will be able to find these specific strains for sale on dowels, but Pleurotus ostreatus is quite easy to find.
Good luck and don't get discouraged; log culture can be really hit and miss.