Moving Extruder Gear Assembly
Hanging up the Bowden system won't fix the problems with printing flexible filament: the filament will still press into the bends of the tube and thus lead to under extrusion. Another issue is, that the flexible filament can compress - and the longer way it has to the melt-zone, the more filament it can "store" on the way to it. These bunched up zones will release suddenly, resulting in pulses of high output and between those under extrusion.

Direct drive (like in a Prusa i3) is pretty much the only way to reliably print flexible materials. You could, with some engineering, move your existing motor to the carriage and turn your Bowden into a direct drive.