What is the proper way to dim LED pods?
Can someone explain these LEDs pods to me, their optimum voltage and
  proper dimming? I think my benchtop results tell the story, but I am
  very unsure.


The current is what controls the brightness of an LED. You need to control the current (somehow). One way to do this is to use a benchtop power supply with a constant current mode. This will allow you to vary the current and set it to a level at which the LED's will turn on. There is one gotcha, the LED will not turn on unless it meets a voltage threshold. 

If the current goes beyond what the LED is rated for, it will overheat, and damage the LED. 

Find the color of you LED module, then look it up on the table, you need at minimum that voltage. For a blue module, you need at least 3.1V at which it will draw 350mA. If you have a constant current supply, you could just set it to 350mA and it would find the voltage (which will be around 3.1V). 


  With 7.8v being the calculated max, how bad is it to run them at 9v?
  There is a difference. I am sure there is some resistance in this
  circuit I am not factoring in.


You need to limit the current, if you set it to 9V the LED's could draw a lot of current, even amps of current which may be too much (you can find out how much current is max for the LED in the datasheet for the color you have). That means you need to calculate both voltage and current if you have a resistor.

There are plenty of circuits to limit current or these besides a resistor

You cal also use PWM to dim the LED's, the rules still apply, you can't go over the maximum current limit.