I believe your Rebecca was the d/o Cornelius Bogard. In this case Bogard is not a mis-reading of Bozard / Bozarth. I remember corresponding with a woman about this Rebecca many years ago. I can't put my hands on the file. It's been about twenty years. It may take me some time to find it, but I'll take another look for it.
On page 345 of Glenn D. Lough's "Now and Long Ago" he made the statement: "The tax returns (first census) for Monongalia County, in 1782, shows Cornelius Bozarth (Bogard), 5 in family; John Bozarth, 6 in family." He changed the Bogard name to Bozarth.
However, Appendix B on page 525 of "The Monongalia Story" shows "Heads of Households - Monongalia County, 1782 (number refers to white souls in each household) - Bogard, (see Bozard) / Bozard, Cornelius, 5; Bozarth, John, 6." [I believe whoever transcribed this list changed the name from Bogard to Bozard.]
John Bozorth, (Jr), his wife Jane Ivers and children: George b. 23 Apr 1774, Valentine, b. ca 1776, John, (III), b. ca1778 and pos Rebecca, b. ca 1780. There is no record of daughter Rebecca's marriage, but the lady who wrote me was sure that the Rebecca who married Ice was a Bogard.
Wish I could lay my hands on my records. If I ever locate them, I'll get back in touch with you.