Consider the Puppia Step-In soft harness
Puppia Harness — Step in Dog Harness
This is what we have - it is extremely easy to put on.
Put their two front legs in, velcro it closed over their back and snap it closed. It is very soft, and fits quite snugly. They can not slip out of it, and it does not "cut" into them.
The lead attaches in the center of the back. The placement makes it difficult for them to get at to bite.