Image jitter when rate-stretching clips

I've recently run into issues with the rate stretch tool when my source material is interlaced rather than progressive. If I slow it down or speed it up, the interlacing manifests as the frame jumping up and down rapidly, which of course ruins the image. Since I've already done a significant amount of editing to the piece in question, is there a good way to get around this issue that will allow me to time-stretch interlaced footage?