Don't use "Y" adapters to combine the _outputs_ of two components! The distortion you were getting with the one set of "Y" adapters was a friendly warning that you were basically shorting the output of the active component with the output stage of the inactive one (even if one of them is turned off). This will cause distortion, but it can also damage your player's output stage over time. Why one set of "Y" adapters had distortion and one set does not, I can't guess, but neither one is a good solution.

If you want to do this on the cheap, and know which end of a soldering iron is the one that gets hot you can solder into the "hot" inner conductor of each leg of all the "Y" adapters a 10K ohm resistor, leaving the shield intact. This will isolate the outputs of both players and ward off any possible damage or distortion.