The 4PDT would have allowed the LED's too. if you go through the selection guide, you might have found something else. We can't read minds yet: i.e. 4PDT switch that looks like x. I've used these flat handle miniature switches and I liked them.
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As an added note, you want to have the relay powered from the ignition switch so the relay doesn't drain power when the engine is off.Here's a tiny little refinement to your circuit: arrange it so that the relay is energized only when you select the lesser-used input source. (In other words, route the most-used source through the NC set of contacts.) That will keep the relay off most of the time and extend its life (and lower power consumption).