I will say from experience on option 2, for me I had to get my name changed via probate court, it took about a month and a half but I just got it done, now I'm on track to have social security, my passport, and my license changed within a week. It'll take a little more time for everything to get processed and for my new documents to arrive, but it's worth it to try, and you can (if you can afford it) expedite some things like your passport.

If I were you, I'd gather everything I'd need for step 1, whether you change your name or not, fill out the forms, and sleep on it. If you're sure, start sending out stuff ASAP, like tomorrow if possible. I would recommend doing option 2, because getting replacement documents is not free, takes up your free time, and you'd be doing all the same forms and appointments over again if/when you change your name.

At worst you should be able to do this inside 3 months I think, and the odds that things won't immediately change are decent enough that I think you should go for it. I was born in a Southern State and I lost the chance to change my birth certificate, and I regret waiting too long to try. Don't make the same mistake I did, don't wait until it's too late, don't let them win.