A better way??????????????????
Hi, Redline.
You may be no digger driver but I think you've picked it in one. There's not a digger that I have ever run, and that's been a few, that doesn't have more power pulling the dipper in than pushing out with it. Hydraulic face shovels, yes, but excavators, NO. And the long reach would have been a bit handicapped in the 'power' department anyway, especially pushing out.
How-wevver, the other commenters have a point too, in that it ought to have been anchored off to something substantial before doing anything to rescue it.