I attempted to reproduce in the manner you described; it did not work. So I created a new document, opened the paperpile sidebar, and banged on keys. I had errors occur at a fairly consistent rate -- much more consistent than in ordinary writing, so I began to suspect, based on what you told me about the cause of the error, that the cause was rapidly-increasing character count.
In rapid typing, the error occurred approximately every 470 characters, standard deviation 113 (sample size 7; I got bored). The range was 315 to 659. In very slow typing, I got to 1321 characters before I got bored and stopped -- no errors. I then moved my cursor to the middle of the (by this point fairly long) document, at least 1000 characters from the end, and typed very rapidly. I got to 1700 characters before I experienced an error. I repeated the test, moving my cursor almost 2000 characters from the end, and typed very rapidly. I reached 2000 characters, then moved my cursor to the end of the document and resumed typing. I got 177 characters, a full standard deviation below the lowest normal result. Finally, I moved my cursor to roughly the beginning of the document and began typing. I reached 3000 characters before the amount of data being entered posed actual problems for the google document, which temporarily restricted my edit access. This coincided exactly with another Paperpile error; I am not sure if they were linked.
Theory: Google Docs is bad at reporting the cursor position when that position is ahead of the last recorded document size, and is slow to update document size.
Interim solution: add ~1500 buffer characters to end of file before beginning work.