These are the brightest backup LEDs that I've installed, hands down.
Luckily you don't have to do all that for the reverse lamps. There are 2 square pop-out covers in the back hatch trim to get to those. It's just easier to do when the whole hatch piece is off so you don have to reach in that hole, especially if you have big hands.
I just noticed the bulbs you recommended are only 400 lumens, there are other reverse bulbs on Amazon that mention ratings of 1000 or 2000 lumens...These are the brightest backup LEDs that I've installed, hands down.
Amazon.com: Elite Vision 194 168 T10 192 2825 W5W Titanium Series LED Non-Polarity 400LM 6000K Bright White for Dome Map Courtesy Door License Plate Cargo Interior Lights (Pack of 2): Automotive
A little on the expensive side, but well worth the price IMHO.
Have a good day.