This isn't surprising - OEM lights have to meet some fairly rigorous specs that your random aftermarket LED simply won't be able to match.
I'm not sure how you could get a brighter backup light. The ones that Honda puts on are fairly bright. For some cars, I know that there are better options available, but Honda usually puts pretty good lights on their cars - from what I've seen, the Honda lights usually are the upgrades! I've been quite pleased with the quality of my peripheral incandescent lights (e.g. turn signals, reverse lights).
Theoretically I suppose you could try to find some sort of higher-wattage incandescent light, but there's no guarantee that the wiring or the housing would be engineered to handle the extra power - this could lead at best to poor performance, or at worst to melted components or even electrical fires. Or, for that matter, that the resulting setup would be anywhere near street legal and/or safe. Or that the bulbs would be optically compatible, which could result in a weird lighting pattern.
As lame as it is for me to say this, the most reasonable thing for you to do would probably be to pick a new tint for your back window. There's no sense putting form over function for something as critical as a car window.
EDIT: Thinking about it again, you might just be able to rig up a motion-sensitive light fixture pointing at your driveway. It would presumably light up when your car approached, allowing for more light without needing to screw around with your vehicle. I'm sure a 40W bulb or equivalent would be sufficient to outline the position of your other car.