I was at the Litvack beit midrash in my local vicinity and was able to find where the Raavad might deal with some of te above questions. That would be in laws of pleas 3:14 and the Tur-Shulchan Aruch Choshen Mishpat chapter 88 law 19. That adds some clarity to the issues however in terms of my specific question about "here it is" that absolves one from an oath of partial admission for a pledge, I still have no answer.--I was at the Litvack beit midrash in my local vicinity and was able to find where the ראב''ד might deal with some of the above questions. That would be in laws of pleas 3:14 and the טור שלחן ערוך חושן משפט chapter 88 law 19. That adds some clarity to the issues however in terms of my specific question about "הילך" that absolves one from an oath of מודה במקצת I still have no answer.