That is exactly how I envisioned it and tried to relate it. As I said the only things I can think of is AC switching on the relay, and fusing. You did mention an AC relay which I hadn't thought of, but I would probably try the standard relay first for ease of availability and cheapness. For simplicity running the DC light off the ignition switch connection is best, but over time may overload the switch contacts. Another conventional relay switched off the ignition to turn on the light would be a better answer, but that entails more wires and additional fusing. The load on the switch in that case would be the minimal current needed to activate the relay. While you were going through that trouble too, you could easily add another switch to turn the DC light off and on if desired. On the relay you can either switch the hot or ground side whichever is easiest to do.
Grounds are grounds, both systems ground to the frame and don't care if they share a connection. I don't mind adding a redundant ground or two even without modifications. For instance, you might think handlebars would ground well, and they do for the most part, but if you think about it the ground path goes through the steering head bearings. I used the bars as a ground for my heated grips since it was so easy and have had no troubles. I figured at the time I did it that worst case scenario was no heated grips, but not a case where it would make me have to push the bike home.
That is part of my thinking always. First simplicity and light weight, then reliability. The system we are designing for your bike as it stands now could go up in smoke and die if shorted out and unfused properly but the machine would still run since the ignition system is completely untouched. I have ridden out of the mountains in darkness using what I could see from my riding buddy's headlight, but I rode out. (turned out to be a bad ground on my headlight in that instance, remember redundant grounds are good things)