What are good ways to dry shoes?
From a theoretical point of view, there are some possible methods to take water out of a fabric object, such as a shoe:


"Replacing" the water for another, faster drying liquid and letting it evaporate;
Squeezing the water out directly by compression and twisting (not usually adviseable);
"Force field" like gravity and centrifugation;
Capilary action (which is what the newspaper does);
Thermal action (sun, heater);
Wind action (free-air, fan).


The last two increase the rate of evaporation, the first by increasing the internal energy of water, the later by reducing the relative humidity of the air layer close to the fabric.

Then (always theoretically) one possible way to dry a shoe quickly would be to force-circulate warm, dry air inside a newspaper filled shoe that has been previously centrifugated/squeezed after being rinsed in warm water with a bit of alchohol.

The problem that still persists is how to actually implement this air heating and circulation without a complicated device or combination of devices...

I use to put newspaper inside as you described, but for the first three stuffings, I squeeze firmly (stepping over if necessary) so that most the moisture is mechanically removed. Then I put extra, dry newspaper and leave the shoes hanging in the open air. Unfortunately, depending on weather conditions, this not always work.