Right power supply for DC motor with load
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.