2 partial plots, need titles

You people are well read and might be able to help me.

There are two books I have been trying to track down for more than forty years, armed only with fragments of plot.

1 SF Begins with the main character standing in a glass crater formed by a nuclear explosion which he has somehow survived, but which has shunted him into another universe and another body.

He was previously a tough-as-nails warrior-type but the new body is of an adolescent wimp. He spends a lot of time with a woman character with (I think) psychic healing abilities and I have a suspicion that sentient cats are involved in the plot. For a long time I thought it was one of Andre Norton's but now not so sure.

2 Historical fiction set in rural England. Opens with a woman being hanged for some crime. She is a singer with strong throat muscles. Three attempts at hanging her are not successful, and she is released.

She has nowhere to go and is given a roof over her head by a pastor/rector/clerical type. They do a number of good works in the village and are both extremely moral people but are shunned and reviled because it is assumed they are "living in sin". There is a character called Mungo who lives wild on the moors.

If either of these rings any bells for anyone I would deeply appreciate potential titles/ authors/ starting points.