Interesting - when I first read this post I thought, hey, I've done this!
https://www.flickr.com/photos/tyron-d675/17837119809But my current setup has LED's running off a center console light - it's not the same. It comes on when the interior lighting is on - not when the dome light is on. So when you dim or brighten the lights inside, those LED's change as well.
For what you want, a footwell light to come on when the dome light comes on, I think the easiest way would be to run another wire to the dome light. The actual switch is at the dome light, so that really determines if that light comes on or off.
Your idea is actually quite cool, I might have a tinker on the weekend to have a try. You'd need a couple lights and fittings and quite a bit of wire that runs up to the dome light. Although I do have the lights in the door when you open the door, I don't think they come on with the dome light, only when you open the door. If they came on with the dome light, I'd just run off them (in any case parallel).
I like my LED lighting, but it's really just ambient lighting, not meant to be intense. But having footwell lighting that comes on the the dome light would be really cool. I'd probably want to do the rear at the same time actually.