3.5mm to RCA cable suggestions.

" I am probably mistaken, but I though there was a problem going from unbalanced to balanced without proper grounding."

You have it right. That's why you can't run a component balanced and SE at the same time. That's why most fully balanced components have either a switch, or jumpers you insert in the xlr jacks directly to run in SE mode. 

" Regarding proper grounding, I would expect that a stereo 3.5 mm to dual XLR adapter cable, such as the Hosa cable the OP linked to earlier, would accomplish that. Presumably it connects the ground of the 3.5 mm plug (the "S" of its TRS connections) to pins 1 and 3 of both XLR connectors. Pin 1 is the ground connection of an XLR input, and pin 3 is the signal pin that should be grounded when an XLR input is provided with an unbalanced signal. "

That's all true, but if a component has a balanced/SE switch, I'm pretty sure you still need to use it.

" Also, I’ve never liked 1/4 inch connectors because in my experience the contact they make can sometimes become intermittent, especially if they happen to be jiggled. "

Same here. Although I'm sure build quality makes a difference, but you don't get a choice on what goes into the component. Just the cable.