I don't recall what your occupation is but I would look into finding something else that is stable and not at risk for lay offs. This guy offering you a job might be good. I'm not sure about your retirement, if it's 401k or a pension. A pension is hard to walk away from. If your company was willing to let a guy go after 37 years, they are likely to do it to you.

My daughter's uncle went through some of the same things you are. He worked his butt off at his job for about 15 years skipping breaks, overtime, on-call, etc. He was in a supervisory position. The last call was when his boss said they were going to hire someone else (below him) at a starting pay than what he worked for 15 years. The boss said everyone would just have to understand. That was the last straw for him. He found something another job. They asked how much he wanted to stay. He told him what this new job would pay him and they said they couldn't do that. He seems much happier with this new job with better pay and they pay more for his health insurance too.