Wow, here comes those eye-twitches I get when thinking of the hundreds of rackets I strung on that machine(middle '70s and early '80s). I don't remember a padded clamp handle, however.
Couple of thoughts. You'll likely make your own decision; but having the clamp handles facing the cross-strings already installed just gets them out of the way while you're stringing the next cross...also makes them easier to operate as you near the last few crosses on a top-down pattern.
That machine really brings back memories! Good find!