I want to be able to "pick up where I left off" in terms of number being played with
You can record where you last wrote to the file.
Are all the records the same size? If so, you could determine the file size, subtract the length of one record, and seek to that position.
but my file will be way too big to read through the whole thing.
Then, a redesign is in order, using multiple files to reduce the size of each.