There are people who use Qimage in conjunction with QTR. You can use Qimage to print multiple files. Qimage also does lines and borders, but at a quick look I'm not sure that you could do precisely what you want that way, however I'm fairly sure that you could with the line graphic that Jon suggests. Qimage does not output greyscale files, but this is not a problem, as you turn CM off and the output file will in effect be in AdobeRGB, which has a gamma of 2.2, and QTR will happily process that.
This workflow involves intermediate files, and so there may be size issues if you're queuing up a succession of large files. In which case you could print a page with the line graphic that Jon suggests, then another and another. In which case you may need a top and bottom line for each image, as I think the printer will advance the paper a small amount after each separate print.
This probably sounds more complex than it really is. Of course if you're on OS X, then none of it is relevant.