Here's how I attached my license plate with all four screws, without drilling into the tub. Why would anyone bother to do this, you may be asking? Well, it's a lot more secure than attaching the left side only like Jeep intends us to do, and also you can now add a license plate frame where you might not have been able to before. Plus, I get a feeling of satisfaction knowing that I outsmarted the engineers who designed it!
I don't have photos for every single step of the process... but once you get into this, everything should be apparent. This whole project shouldn't take more than 30 minutes and cost you less than $5 in hardware.
Here is the key to the whole project: it's called a Tee Nut, and you'll probably have to go to a real hardware store for these - not a Home Depot or Lowe's. I used the 3/8" size ones (you will need 2, and corresponding license plate screws to thread into them. I bought 1" long screws, and then cut them down to the exact length I needed).
First, remove your license plate bracket from the Jeep. Don't forget those screws underneath, the bumper makes them hard to see and get to. The tee nuts will go through your license plate bracket from behind, on the right side. Remove the plastic pin sticking out of the frame, and drill a hole to accommodate the tee nut in the exact same spot.
You will need to grind the edge off of the tee nut so it will fit, this will also keep it from rotating when you tighten the license plate screw. The tee nut will be inserting from behind. I put a piece of tape on it to hold it in place while assembling everything. Now you can see why the tee nut is necessary - any other fastener will end up digging into the paint on your Jeep's body.
Most license plate frames will not fit inside the lip of the factory plate bracket - they can only sit on top of it. So the fact that the tee nut now protrudes a bit on the front side of the plate bracket will actually play in our favor. You don't even have to remove those tabs on the right side that hold the edge of your license plate. If you wanted to, you could even go back to the stock mounting method - the factory license plate bracket is not ruined in this process (useful if you're trading in, and want to keep your license plate frame).
You will need to add some kind of spacer around the tee nut (on the front side), to keep the license plate from rattling around between the plate bracket and your license plate frame. it could be some small piece of plastic, some washers, or whatever. On mine, I found some small plastic spacers which I drilled out to the appropriate size, and stuck in place with some silicone while I reassembled everything.
Before mounting the plate bracket back onto your Jeep, it's important to check the length of the screws you will be using on the right side (which will be threading into the tee nuts). MAKE SURE they don't go too far and dig into your Jeep's body/paint! Ideally, they should not protrude out of the back side of the tee nut when everything is assembled and tightened down. If you can't find the exact length of screws that you need, you may have to cut some down.
Now it's time for final assembly. Reinstall your license plate bracket back onto the Jeep - check clearance behind those tee nuts one more time! If everything is ok, next comes your license plate/frame. On many license plate frames, the plate will actually snap into the frame. Place the plate and frame on top of the protruding tee nuts/spacers. On the left side, use sheet metal screws of the appropriate size and screw right into the plastic of the factory license plate bracket (use the existing holes). On the right side, I added a drop of blue Loctite before threading the screws into the tee nuts. Below is the finished project... I added the screw covers that came with the license plate frame. I'd suggest checking everything periodically to make sure none of the fasteners loosen. I've done this to two Jeeps, and both have held up perfectly for 7 months now, so I'm confident that this method is secure.