I do a yearly workshop on cutting windows and framing using simple tools, rather than hind matt cutters. ALtho, I have one I find it easier to use a metal straight edge, healing mat and a logan cutter, just as you suggest.
In addition the self healing matt is clamped to a 3/4 inch piece of plywood and I like to clamp the straight edge down. Clamps can be found for a buck apiece at Home Depot vs $6 at various art shops. The clamping helps me as my "old hands" are not as strong to hold every thing together.
Works like a charm.