Problems with your stock system cutting out with higher volumes or just the output of the line output converter?
If the latter, sounds like it is being way over driven. Adding a series resistor is not enough if over driven, helps to have an oscilloscope so you know what peak voltages you are dealing with. Need some form of an attenuation, like a voltage divider. When dealing an input to an amplifier, if it didn't have a level control, would add a dual ganged pot so it would have one. With balanced outputs, can't ground any of them.
Remember when radios were just that, radios, have two of them, a single DIN in one vehicle, and a double DIN in another. All kinds of choices.
But not in these newer vehicles not only a radio. but part of the anti-thief and alarm system, on the data link, and also used to program functions in the BCM. Pretty much stuck with stock or an exact equivalent. And every vehicle is different when for a short period, they were all the same.