Hey mate, before cutting things or spending any money maybe just remove the bridge and run the long rule all the way to see how things are. Even with the bridge in place you should still be able to place it at a slight diagonal angle for the whole length.

Another idea is to do the capo at 1st fret and with strings at proper pitch draw the low E down at 12th and again at last fret which should be 22nd on a LP. Check how much gap is under the string from each of those reference points back to the capo'd spot. If all of this reveals a dead flat deck the problem will be elsewhere.