A lot depends on how accurate you need these strips to be. Since you stated 1 1/8", rather than just 1", I'm guessing that accuracy is important. You won't get an accurate cut with scissors or rotary cutter cutting through a large number of layers. Even the largest rotary cutter isn't designed for that. And unless your batting is very dense, it will not keep its shape very well. If accuracy is important then I would just continue with cutting roughly 4' lengths, and slice them up with a rotary cutter and ruler, cutting no more than one or two thicknesses at a time. 240' divided by 4' per slice is only 60 slices - will be done before you know it, if this is all you need. If you mean that you need to do this multiple times, then I feel for you.
