I have the same dimming lights issue at red lights etc.......when I gas it some the lights are fine....
Now, I have a cam ,so my idle is pretty rough which is probably part of it.
New, VR, new alternator, etc....went over the ground connections, added new ground straps between the ECU, VR and the engine, which in turn has the ground cable to it......I dont have the issue of batteries dying out though.....
I know this isnt much help.....just commiserating. LOL
You dont have any accessories that may be draining the battery when sitting, do you? Like an alarm or radio or something?