Cross Fade Arbitrary Number of Videos with ffmpeg Efficiently

Question

I have a series of videos named 'cut_xxx.mp4' where xxx represents a number 000 through 999. I want to do a cross fade on an arbitrary number of them to create a compilation, and each fade should last 4 seconds long. Currently, I'm doing this with Python, but I suspect this is not the most efficient way:

import subprocess    
def get_length(filename):
  result = subprocess.run(["ffprobe", "-v", "error", "-show_entries",
                          "format=duration", "-of",
                          "default=noprint_wrappers=1:nokey=1", filename],
    stdout=subprocess.PIPE,
    stderr=subprocess.STDOUT)
  return float(result.stdout)

CROSS_FADE_DURATION = 4

basevideo = 'cut_000.mp4'
for ii in range(total_videos - 1):
  fade_start = math.floor(get_length(basevideo) - CROSS_FADE_DURATION) # new one
  outfile = f'cross_fade_{ii}.mp4'
  append_video = f'cut_{str(ii+1).zfill(3)}.mp4'
  cfcmd = f'ffmpeg -y -i {basevideo} -i {append_video} -filter_complex "xfade=offset={fade_start}:duration={CROSS_FADE_DURATION}" -an {outfile}'
  basevideo = outfile
  subprocess.call(cfcmd)
  print(fade_start)

I specifically remove the audio with -an because I'll add an audio track later. The issue I see here is that I'm compressing the video over and over again with each individual video file I add to the compilation because I'm only adding one video at a time and then re-encoding.

There should be a way to cross fade multiple videos together into a compilation, but I'm not sure what this would look like or how I would get it to work for an arbitrary number of video files of different durations. Any idea on what that monolithic ffmppeg command would look like or how I could automatically generate it given a list of videos and their durations?