Just a thought.... You may want to do a little checking for termite damage and/or evidence of specific compression of some wooden support structures. You can sometimes tell where the compression or settling is taking place by checking which doorway openings are getting out of square. Sometimes doorway openings that run in one direction get out of square while those that run perpendicular to that are not out of square. And, sometimes, the settling is not in the actual foundation but instead is near the center of the house in the area of a main support beam.
One of the reasons for checking this is, of course, to prevent further termite damage if that is what is happening now. And another is that it may be possible to add some supporting posts/jacks in the basement when a beam is located -- and maybe even jack things back up a little to help straighten out the doorways and prevent further problems.
In other words, the doorways getting out of square may be indicative of a problem that you can fix while preventing further deterioration, and not just "the house is still settling".
But, back to your original question -- I like the electric planer idea since you have a lot of planing to do.