What joint acceleration values does the robot realistically use? In the KUKA docs I haven't found any information at all so far and I don't know if the range is something like 250-500 °/s² or more like 5000-10000 °/s² or anything in between. I only need a rough estimate to know the range I am working with.

There is no explicit bound for this. Since we are talking PTP moves here the limitations come from the robots dynamic model. The dynamic model restricts gear and motor torques. In this case $ACC_AXIS[] does not limit axis acceleration directly but the torque available to accelerate/decelerate each joint (the maximal values for torques are stored in robcor.dat inside the dyn_dat[] array. But the documentation of the dyn_dat values are a company secret of KUKA and not publicly available). How much torque there is available depends on the robots state (position, velocities, accelerations, loads, ...). Lets assume a motor can generate a torque of 40 Nm. Holding the robot and its current position (assuming for simplification positions, accelerations are zero) requires a motor torque of 27 Nm than a value of 100 in $ACC_AXIS[] means the robot will try to use 13 Nm for acceleration. Basically everything that can be used up to the maximal torque value. But since the robot is a coupled system this might not be the resulting acceleration you will see in the end. Since the calculated trajectories of the robot are time and phase synchronized over all axes it might be that another axis is the actual limiter for the overall torques. In this case all other axes are "slowed" to fit the limiting axes in such a way that all axes start moving and finish moving at the same time (this is an important feature that no matter what the user programs for VEL_AXIS and ACC_AXIS the resulting movement of the TCP in Cartesian space is always the same).

To use accelerations on joint level in rad/s^2 you would need to deactivate the dynamic model. But this is not recommended because it is than a lot easier to destroy your robot and in your use case you would also see even more unwanted oscillations.

If you want full control over how the robot accelerates and decelerates yourself the only option I can think of is using the RSI package.

Another possibility to get closer to commanding direct rad/s^2 values would be to use spline motions in combination with adding additional restrictions by means of $SPL_VEL_RESTR. If I remember correctly you can add joint specific restrictions for axis acceleration in there. In that case $ACC_AXIS is applied as percentage value to both (torque limit and joint acc limits). Joint limit acc then is defined by the $RAISE_TIME[] the time it takes to acc from stand still to maximal velocity for each axis. In KRC2 $RAISE_TIME was directly inside R1/$machine.dat but for KRC4 this changed and the info was moved with tag RampUpTimeUnderLoad into the motor configuration xml-File of the specific axis.

Maximum axis acceleration - General Discussion of Industrial Robots Only - Robotforum - Support and discussion community for industrial robots and cobots (robot-forum.com)

Of course for getting a better performance with less or minimal oscillations the would be other options using available features of the robot controller but as I take that is not what would be a feasible solution justifying a masters thesis.

Last but not least what you also could do is just "measure" the resulting accelertions by using the built-in oscilloscope function (aka trace) inside the KRC. You can record the resulting axis acc by configuring the correct channel you want to record and than plot the result using either WorkVisual or the Tracetool found in any KRC installation in the C:\KRC\UTIL folder. So use $ACC_AXIS just to "scale" the input but what the resulting axis acc you get is only defined after recording the values and looking at the trace plots.

The data sheet for the KR150 2700 extra we use states the maximum speed at 150kg is:

A1: 123 °/s, A2: 115 °/s, A3: 120 °/s, A4: 179 °/s, A5: 172 °/s, A6: 219 °/s

Am I correct in assuming that I can safely set $VEL_AXIS[] to any value that is equal or smaller to these?

The value entered for $VEL_AXIS[] is a percentage of the maximal value. So 100 means maximal velocity. The actual maximal value is given by $VEL_AXIS_MA in motor revolutions per minute inside R1/$machine.dat. If you want to calculate maximal axis velocities you need to also consider gear ratios RAT_MOT_AX[] and axis couplings $AXIS_COUP[,] inside the same file.

External Axis (on Rotary Table) - Rotation Speed Control - KUKA Robot Forum - Robotforum - Support and discussion community for industrial robots and cobots (robot-forum.com)

(its basically the same for robot axes).