David Weaver
I've got saws with hands down toward the middle and the more modern type (Both short and long), and the lower handle works fine with teeth filed to accommodate for it (just a little more aggressive).

My first backsaw kit was an english type with a heavy spine and a 16" plate with the handle down almost as low as yours and 10 points. Like you say, it's an adjustment to get it started, but it takes just a little bump, and anything it's too aggressive for is something I wouldn't saw with it, anyway.