How to obtain high resolution prints in a shorter period of time? When I've printed an object I've had to choose between high resolution and quick prints.  What techniques or technologies can I use or deploy to speed up my high resolution prints?
You could experiment with slicing. For example, you might not need high resolution all over the object, but you can speed up some straight parts by using greater layer high there. See a part of Slic3r manual about such thing.

It is also possible to print thicker infill every Nth layer, see Infill optimization in Slic3r.

Other slicers might have those features as well.