Cost of Living negotiations with remote job?

I am currently in salary negotiations with a large, well-known company for a remote Data Scientist role. I have 5 years of experience and am currently working on my master's. I'm currently making $112k, in part because of the high cost of living in my company's area. However, I became remote about a year into employment, and have recently moved to an area with a lower cost of living (Miami, FL).

Now I have an offer from a new company, offering a slightly more lateral move than I was hoping for at $120k. I originally said I was only looking for jobs at $125+, but the in-house recruiter says that's too high for Miami.

What should I say to negotiate this higher? Or simply am I priced too high for my new area?

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