Ultimately, you'll need to tie all the grounds together or else you'll start to generate ground currents wherever it is possible to do so. When this occurs thru a signal line, you can start to fry low current drivers which gets messy.
Now, when you do set up a ground current, you're running the risk of setting up a ground current from the P'S's with surplus current to the one current hog that is asking for lots of current at that point in time - the thing will try to suck power from whereever it can.
Bigger P/S won't hurt. You might also add more capacitance for extra surge capability.
Where you add the capacitance may be something to play with. Try adding it (large cap) near the servo amp. You can use heavy wire from cap to amp and amp to motor (IE 12 or 14ga) and small wire from P/S to cap (18 ga). This way, you'll deplete faster than you can replenish. You can also monitor voltage to see where you need to add extra OOMPH.
At some point, it should become self apparent if you're gonna need more caps or more P/S capacity to keep up....
A volt meter across the caps will also show if and where voltage is dropping which is clear indication that P'S can't keep up with the demand being asked for at that point.
Like Tim Allen says, "you need more power, grunt groan".
Like racers say, "too much power is ALMOST enough".....
Effectively, the motor with the most load will ask for the most current. Feed it what it wants and it will move/cut at the speed desired. If not, things won't move as desired/intended....


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