Like others said, definitely a slow process. Sign up your new, necessary accounts to your new address and port your old existing accounts over a day at a time.
Once you have ported an account over you can mass delete emails relevant to that service. You could also keep a log of everything you have ported. Or both.
You can also straight up delete the accounts you don't need anymore, if thats part of your goal, or something you would find satisfying. Same thing - deleting all of the emails relevant to it afterwards. Eventually you will be able to scroll through years of email without seeing anything you are worried about losing.
Doing this passively, with little time investment over the course of a few years.. one day you're done and ready to cut the cord.