When I attempt to calibrate extruder steps the increased values don't correspond to physical increases I am attempting to follow these instructions to calibrate the extruder, however when I increase the value for DEFAULT_AXIS_STEPS_PER_UNIT the change in physical output does not correspond with the changes.

I started by testing how much filament goes through the extruder when sending G1 E100 F100 to my printer, instead of the 100 mm I get about 38 mm (#define DEFAULT_AXIS_STEPS_PER_UNIT   { 80, 80, 400, 93 } in Marlin). I increased the value to DEFAULT_AXIS_STEPS_PER_UNIT   { 80, 80, 400, 149.73 } which should take it to 100 mm, when I tested the physical output the increase was only negligible so I repeated the calculation with DEFAULT_AXIS_STEPS_PER_UNIT   { 80, 80, 400, 387.8007 } as the new value. The new physical output is about 64 mm, I think this suggests a mechanical problem rather than a firmware configuration problem, but I am not sure where to go from here.

My printer is the Ender 3, running Marlin 1.1.9 with a BlTouch and an aluminium bowden extruder mod 

(installed after the extrusion problem began).

Any help you can give will be greatly appreciated.
Mechanical?

You basically answer your own question that there could be a mechanical issue.

If 93 steps gives you 38 mm, to get to 100 mm, you need to divide 100 by 38 = 2.63 times. This implies that you need 2.63 x 93 = 244.7 steps/mm (not 149.73).

You even tried close to 400 steps per mm to see you are not extruding 100 mm of filament. This implies that you are either missing a lot of steps (increasing the stepper current or increasing the temperature of the hotend would help out) or the extruder gear slips on the filament (increasing the pressure on the extruder gear and filament could solve this).

Or not mechanical?

Furthermore, it could be another issue than mechanical. If your extrusion rate is too fast, the stepper might not be able to cope the high speed and miss steps. I have had this before with a too high of a retraction speed.