I think you might need a few things clarified.

The microstepping setting simply controls how many steps the drive takes on the input, compared to what it outputs. A more accurate description would be step-multiplier/ratio.
I'd guess the drive output will never go above 16 or 32 microsteps, as above that resolution, it makes no difference to motor smoothness, and it certainly does nothing for accuracy, as microstepping is by nature inaccurate. Due to the very nature of microstepping, what it's essentially doing is holding the motors rotor between two electromagnetic springs, so position cannot be guaranteed other than to the nearest step.
Personally, I would never run above 32 microsteps, as there is no real benefit.

In terms of current. In electric motors, current = torque. Reduce current, you reduce torque. Less torque means you can't accelerate as fast. It also likely means you'll hit the stepper motor/driver bad resonance point and stall at a lower speed.
Too high a current could cause failure due to overheating, but I'm sure you would have noticed if the motor had heated up.
As Clive says, stepper motors can run hot. 80degC after running for a long time is acceptable, but if they get that hot in a matter of minutes, then you've got a problem.


One thing you could try, is unbolt the motor, and separate it from the screw (that style of coupler will simply pull apart)
Try spinning the screw by hand, to see if it feels smooth
And run the motor with no load.


Having watched the video again, it could just be the fact it's using a big stepper motor.
It does sound like the stepper motor vibrating, and being amplified through the relatively light weight rig. There does seem to be a variation in sound level per revolution, but probably nothing you'd need to worry about.

A solution would be either a small servo, or possibly a smaller stepper motor with some gearing.
Although given you don't need high precision, I wonder if the existing motor could be mounted using some kind of anti-vibration mounts to isolate the motor vibration from the rig.