Again thanks! I think there was a typo in the post. You may have meant:
And in that case you are of course right---same equation.
My main focus needs to stay on Rovelli's April paper, but I will keep intermittently chewing on the two Ashtekar papers and trying to understand them better. Ashtekar has a different perspective and has been a formative and greatly influential QG figure over the long haul. I have to pay attention especially to his overview of the field. Differences in formal detail can work themselves out---I can probably get along with just Marseille notation. But I have to try to assimilate Ashtekar's vision. Both the papers you pointed to have introduction and conclusion overview sections that I'm finding helpful that way.