Next you are going to want to use a sharpie to trace the new fabric (no worries the edges won't be shown on the finished product) then cut it out with some fabric scissors:
At this point I got a little carried away and forgot I was doing a write up HOWEVER you are going to want to spray the glue onto the door piece (tape off sections that you don't want glue on) and let it tack up, then apply your new piece of fabric, make sure you are lined up pretty good as this glue can be unforgiving after contact... Tuck it into the corners and smooth it on from one end to the other to prevent air bubbles (pretty much like applying baller JDM stickers...)
Once dried enough to handle (5 minutes or so) we want to reapply the two pieces of door panel:
Now here's where it can get dangerous, we need to drill for our new attachment screws HOWEVER we have only about 3/8" before you will be drilling out to the visible side of the panel... Some of them are more forgiving than others, best way to approach this is to look on your own and get some good depth perception, as each of the 11 are more forgiving than others...
CAUTION: To best determine depth, wrap a piece of electrical tape leaving roughly 1/8-1/4" of drillbit exposed, this will allow you to know how deep you have gone, thanks WagonR
Here are my screws in place, if you can find screws with a wider head to secure it do that but these are what I had to work with...
And voila!! New door panel to match my UN-BLUED interior