Well, the man page does say stuff can't be used for large inputs:
stuff [string]Stuff the string string in the input buffer of the current window. This is like the "paste" command but with much less overhead. [...] You cannot paste large buffers with the "stuff" command. It is most useful for key bindings.
But it does hint at paste:
paste [registers [dest_reg]]Write the (concatenated) contents of the specified registers to the stdin queue of the current window. The register '.' is treated as the paste buffer.
readbuf [-e encoding] [filename]Reads the contents of the specified file into the paste buffer. [...]
I tried it by pasting the screen man page (2600 lines, 166 kB) to an editor:
screen -S test -X readbuf /tmp/screen.txt
screen -S test -X paste .
and got the identical file back after saving it, so it seems paste might work better. This does have the downside of requiring more than one command, though, and I don't know if it can be done without passing the data through a file.
In any case, I'm not sure if pasting data through screen is the best way to send commands to a running server, but I don't know if Minecraft provides other ways to send commands than stdin.
One solution which I've seen done with another game server is to redirect input to the server from a pipe, like
tail -f inputfile | ./whateverserver ...
and then, if you need to issue commands to it, run echo some command >> inputfile. This should work similarly to stuffing input with screen.
Note that any solution like this that stuffs commands automatically to a single input has the problem that unless you're careful, multiple commands being sent at the same time may get mixed up. Really, this would need locking.