BK Precision 1550
This is a switching supply.
The up-down adjustments would make this a non-starter for me.
CSI3005X5
A whole bunch of companies re-brand this unit. They're actually fairly decent. The voltage pot is a 10 turn, the current limit is button-driven in 0.03A increments.
The most common resaler of the power-supply is MPJA. It also comes in a bunch of voltage and current ranges: 0-30V 5A, 0-60V 3A, 0-120V 1A.
One thing you can't see in the pictures is that the unit has a set of screw terminals in parallel with the output banana jacks, below the cover plate labeled "EXT OUTPUT". If you need more permanent connections, you can use the screw terminals.
The schematic for the whole supply is available. This makes it enormously more repairable (and hackable) then ANY of the others.
BK Precision 1671A
The funky extra output connections on this make me nervous (speaker terminals? really?).
I would guess that the potentiometers are single-turn, both from the artwork on the case near the knobs, and the fact that it does not mention multi-turn knobs, as that's normally a significant selling point at this price range.
On the whole, If I had to choose from the supplies listed, I would wholeheartedly recommend the CSI3005X5, more because the alternatives are considerably worse.
Anyways, I would say that even if you don't think you need a floating output power supply (what you really mean when you discuss a separate earth terminal), you almost certainly will find it useful in the future, so I think you shouldn't dismiss it. Just being able to string multiple power supplies in series for higher output voltages is tremendously useful.
Best Answer
The load has an inertia of 0.645 kg-sq meter, and which looks like it is too big to accelerate fast enough for your motor (although I may be mistaken here).
If you can, will you please run your motor at no-load (not connecting anything to the shaft), and see the results (V,I and RPM). Adjust the voltage such that you get around 1200 RPM. From the spec sheet of the motor you provided, 1200 RPM at no-load will run when you apply 12 V. It would help me and others in helping you solve your issue.
Also if you could include the data sheet of the lab bench power supply it would be helpful, as I think that the problem is the internal resistance of the power supply. I tried searching but couldn't find it.
If the internal resistance of the power supply is high, then there will be a large voltage drop across it when you draw high current, and you will not receive the required voltage. That however is just one of the possible causes. Other causes I cannot determine as of now.