Is There a Free Way to Fix Photo Dates?
Yes. exiftool is free and excellent if you are comfortable at a command line. Otherwise there are free allowances.
exiftool is free, open source and does everything. The cost is learning it: you write the command that matches your situation, and Takeout exports need a fairly involved one to handle the sidecar naming.
If the command line is not for you, most desktop tools let you do a few hundred photos free so you can see the result before deciding.
Takeout JSON Metadata Fixer is free for your first 500 photos with no account and no time limit. Unlimited is $9.99 once, not a subscription.