Bear with me here as I work to reconstruct the Rices families of Devon from the parish records. I'm sure to make a lot of mistakes and will no doubt end up changing my mind a few dozen times about how they fit together.
One thing that occurs to me today as I look at the records is that Christopher Phillips married Agnes Rice in 1613. Other genealogists have said she was the Agnes born 1591 in Barnstaple. So, he was age 48, a widower. She was 22. Not impossible.
But, suppose that's the wrong Agnes. Could she have been the Agnes Gille who married John Rice at Barnstaple in 1595? If she was, say 22 at that marriage, she would have been 36 in 1613 when an Agnes Rice married Christopher Phillips. And, she would have been age 39 and 41 when her two daughters with Chris Phillips were born -- apparently the last of his children.
If correct, this would make immigrant John Rice potentially the half brother rather than cousin of the Hannah Phillips who settled at Dedham.
Problems with this idea --
First, I find no death record for this John Rice. Actually though, I don't find death records for most of the Rices named at Barnstaple. They probably died in surrounding parishes.
Second, a John Rice, son of John Rice, was baptized in 1631 at Barnstaple. Don't know if the father was the same John Rice, but the baptisms at Barnstaple suggest there might have been only one. If John 1631 was the immigrant, he would have been only 18 at the time of his marriage.