RHPs are very light and easy to install. They often come with crews that you just screw into the top of the enclosure. The lightweight aspect means they won't pull away but if you are concerned there are always bolts and nuts you can use to secure it down (honestly not needed). The hardest part for some people is the snapping in the plug to the power cord. It often comes with instructions and really it is something you just put the cord in and squeeze shut. Once you see it, it becomes really easy to do.
I am going ot go off the common placement and one that Bob at pro - products recommends. You place the RHP on the warm side of the tank and place the probe of the thermostat on the cool side. You can either string the probe through the vents and down the side or drill a hole near the bottom and place it there. You want it slightly above hte floor to prevent the snake form sitting on it or relieving itself on the probe. It is fine to have it dangling down on the side of the tank.
What you do is dial in the temps so the cool side is where you want it. The idea is then the warm side will get to the temp you want and the cool side will be the ambient you want. You might need to adjust it to find the best compromise between hot and cool side and that is best adjusted using an infrared temp gun to read temps and adjusting the thermostat to where you need it.
you really would not need the UTHs any longer but if it gets really cold in the winter you might want to keep the warm side one for belly heat. It won't hurt anything and as long as you have it controlled via a thermostat it will not over cook your snakeI would remove the one from the cool side or just unplug it.
You also should not have problems with the led if they are installed on the back side. you should be able to install the RHP more toward the front of the cage and it will still work as intended.
Good luck and as long as you have one of those IR temp guns to dial in temp reading on the thermostat, this won't be an issue.