How old is your machine? What is it reasonably capable of doing for feedrate, according to the spec sheets?
If you machine an outside square corner, do you get a bellied out corner? Does it occur equally in both X and Y? You'd need to machine different test cuts to determine this because the axis making the straight cut is the one that will experience the overshoot, in other words, the overshoot is confined to moving axis, you most likely won't see both axis overshoot simultaneously. You need to be sure that both axis are behaving with the same degree of error so that you know if one needs to be tuned differently than the other, because altering the tuning of one axis can affect how circular your circular interpolations are.
Having said that, I don't see a figure for your derivative gain, I'm not sure if Loop gain = Derivative, it may be different.
In the tuning I have fooled with, I am led to believe that the proportional gain is the one you would alter to improve the stiffness of response of the servo. Integral gain is fairly touchy, and it kind of counters the effect of the proportional. Derivative gain is kind of a damper on the ringing effect created by sudden stopping of the motor at position. It is not so sensitive to tweaks.
You'd have to double check that your Loop gain might actually be the amplifier gain which may increase the max current flowing in the circuit. It may (or may not) be safe to alter this, but giving the motors a bit more juice may also detune the system a little bit, because it will affect the rapids, and accel/decel without giving you better contouring response.
It may also be the case that your PID tuning is fine, but the accel/decel ramps could be set more aggressively. The only downside of boosting these ramps would be servo amplifier overload faults. I think for testing purposes, it is probably okay to bump the accel/decel rate until you get to the point of amplifiers cutting out on overload, then back off a little bit. You need to test accel/decel with moves that are long enough to allow the motor to obtain full speed (in rapid). This might be 5 inches (or more), depending on how much power your servo system has.
Maybe Al or somebody will happen along with some more insightful comments.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)