Mapping image to drone video, perspective issues

By far the easiest thing to do with that shot is to use Mocha AE and do corner pin tracking. It will take less time and be 100% effective. 

Here are the basics:

Create a new comp from your trimmed footage, add Mocha AE to the layer, open Mocha and set up the tracking. Because there is a lot of lens flare and moving patterns in the footage I recommend that you start in the middle of the shot, add a spline to each corner using the + spline tool, then add a bigger spline in the center so all of the splines are on the same layer. Then make sure perspective tracking is selected and track back to the front, then jump to the first keyframe and track to the end of the shot. This is what the setup looks like:

Sorry about the cropped screenshot but you get the idea. The next step is to add a reference image and adjust the surface. If you pay attention to the cursor it is pretty easy to line up the corners of the reference image with the corners of the sign. It is going to be easier to replace the boarder so make sure that everything is covered.  Now the Mocha project looks like this:

When the tracking is good, save and close Mocha. Then all you have to do is drop your new sign into a separate comp, make sure the new sign includes the border and resize the artwork so that the comp containing the new sign and the original comp is the same size. That looks like this:

The last step is to add the new sign comp to the original comp timeline, Select Mocha AE and import the tracking data from layer 1, then apply the tracking data to the New Sign nested comp. A little color correction is all that is left. I just added a lens flare to the New Sign comp to kind of fake it. The result looks like this:

It took me about 10 minutes to get this far using a screen capture of your sample video.

There is a lot of good info available on the Borris FX website on using Mohca AE. Don't be afraid to use the Search Help field in the top right corner of AE and become familiar with the user guide.

The proper technique for replacing the digital billboard depends entirely on the shot. It sounds like you are trying to use Camera Tracking. The other common approach is to use Corner Pin tracking either by running the shot through Mocha AE or by using the After Effects Track Motion > Corner Pin Tracking tools. Seeing the shot would help us help you.

If you are doing Camera tracking the first step is to trim the shot to just the footage you are going to use in the final edit. The next step is to select the Motion Tracking Workspace. The third step is to select the footage layer in the timeline then select Camera Track. Most of the time enabling the option for Advanced Analysis is the only change you need to make to the default 3D Camera Track UI. The comp would look something like this:

When the analysis is complete the very next step is to set an Origin and Ground plane by selecting as many points as you can on a flat surface in the shot that you want to use for the ground. You do that by dragging a selection around tracking markers and making sure that the target looks like it is attached to the surface of the ground. That looks like this:

You can see how I have selected points on the flattest part of the road they are building and I'm avoiding the points that are not on the same surface. You hold down the shift key and drag your selections around. Then you hover over the center of the target and position it where you want to origin (0, 0, 0) point of your comp to be. When you have the target selected you set the origin and ground plane, then immediately right-click again and create a camera and a solid. This solid you are placing is critical in making sure that you have selected good points and that your tracking data is accurate. 

If you have properly selected your Origin and Ground plane when you create the solid and the camera the Z-axis of the solid will be pointing straight up. You can select the solid layer that has been created, rotate the layer in Z to line it up with the geometry on the ground and then scale it and add a grid to give you a really good reference layer to check the camera track. That looks like this for this shot: 

If you have a good camera track and made a good choice the reference solid will track perfectly. 

The next step is to find some points on the surface you want to use for your new element. This would be your new LED sign. You do that by selecting the footage layer again and selecting 3D Camera Track in the Effects Control Panel and then scrubbing through the footage until you find a point where you have a fair amount of tracking points on the surface you want to replace. Here's what I could find on the wall on the right side of the frame:

I scaled down the Target Size (see the 3D Camera Tracker settings) and found these four points. The target looks good so I added another solid as a reference. Now I am almost done. If I had not been able to find points on this wall I would have been able to adjust the reference solid with the grid until the edge touched the wall, then added another 3D solid for and moved it over to the wall. That is just one reason you should always set an origin and ground plane and set up a reference solid. 

With the reference Track Solid 2 added to the scene I'm ready for a final check. Everything looks pretty good but there is a slight misalignment with the wall when I adjust the scale and the Z rotation to line up this reference solid.

I hope that I can fix this with the Y rotation alone. After a bit of tweaking and moving the layer back in Z by about 10 pixels this reference solid is tracking perfectly with the wall. 

Sometimes you can get away with leaving out some of these steps, but most of the time, the two or three minutes you spend setting up the origin and ground plane, adding the reference solid and adding the grid, and tweaking the position of the reference solid is insignificant when you compare it to several failed attempts to get camera tracking to work. If you have a good origin and ground plane and reference solid you can always position the replacement layers where they need to be. If you do not select the right points the first time you can easily spend the better part of a day fiddling with the shot.

The last step is incredibly easy. Add your replacement image, make the layer 3D, hold down the Shift key and Parent the replacement layer (your new sign) to the second reference solid. It will snap to the same position and be locked into position. Then you can either set both your reference solids to guide layers so they won't render or turn them off and you are ready for the final color adjustments and rendering. The final would look like this:

If you can't get it done following those instructions then you need to post the shot for us to see and you also probably need to start here: Learn AE