Why would you need several offers if the new job will be paying less than your current position? Can’t you just tell them how much you make and ask them to match that in equity?
I think the main draws at a startup for a post-FAANG senior engineer are feeling good about the product they build (more useful to the world than FB's ads) or the role/environment (less bureaucracy and org process). I am sure there are many exceptions, but I suspect that after 10 years in a senior role at a FAANG money stops being the most important thing you need from a job. My 2c.