You're right in that the final version will have a fixed chunk size. This is simply an exercise to figure out if I can do it or not, and then I'll change the code accordingly.
I am not very experienced with buffers, and the code I pasted is from an earlier answer on perlmonks to a very similar question that I asked, only they were dealing with smaller files. I'll see if I can figure out how to adjust the loop and use fixed chunk sizes.