Are loops in ground planes acceptable?
I could break the ground pour where impedance matters least and strategically place a bunch of vias to the second ground layer to get a nice star shaped ground design.


Without seeing your schematic, we can't say whether a star ground is appropriate or not. 

If you do go this way, remember you have to also provide return paths for your signals. Not doing so could itself produce a loop capable of radiating or receiving emi.


  just keep the copper pour as it is and sprinkle a bunch of vias to lower the overall impedance.


Without knowing enough to be absolutely certain, I tentatively recommend this solution.

If the top layer copper is well-connected to bottom layer copper, they essentially act as one copper region and you have no loop to worry about.

You may have a small window through the board that isn't plugged with copper, but at 13 MHz the wavelength is 23 meters. A loop with a few mm diameter is not going to pick up this frequency with any efficiency at all.