I've seen a LOT of similar machine bolted to wooden bases, with no issues. Along it's length, wood may be more stable than aluminum.
If you don't have enough torque to move the machine as fast as you are trying to move it, then you'll lose steps, regardless of the current. There's no chart that tells you how much torque you need to move at a certain speed, so trial and error is the normal technique.
I had you lower the current to see if the motors ran smoother. If they seem to run the same, then increase the current back to where it was. You can probably try the 5.83 amps and see how it works, but watch for hot motors.
Note that steppers can safely run well over 100°F. If you can hold your hand on them for 5 seconds, then they are not too hot.
One thing that's important when testing is to not change a lot of different things at one time.
Change one setting, and do a lot of testing to see the results.
Repeat.
One thing you might want to try is a different motor, like this one.
https://www.automationtechnologiesin...lat-381-oz-in/
You can get one and see if there's much difference between the ones you have?