Sorry organicadan94, this is just not true. Stirring is vital, especially on scale. It promotes vital heat transfer throughout the medium, without which you may end up with an adiabatic runaway decomposition. Especially in this case.
As to the OP, a mechanical stirrer is obviously the best option, if you can borrow one do so, there must be one somewhere.
Why distill the DMDO anyway, I'm not sure it is thermally stable at the acetone BPt. I would check that out before you do it, as a 4L scale is large for a lab scale prep.