Isn't there a way to just pay someone to do this for us??
Sure, by all means: feel free to pay me, send me your wallet, and I'll send your funds to another address. Risks: trusting me, trusting the email/upload you use, trusting my computer, trusting your own online computer, trusting malware anywhere in between.
It's possible. And it sure as hell isn't recommended!
There has to be some legitimate business that does just this( recovers people's Bitcoin
Talk to Dave:
Bitcoin Wallet Recovery Services. And watch out for phishing sites!
from their zip drives) so they don't have to download the entire Bitcoin Core or whatever that is.
Who still uses ZIP drives? But that's a different problem than downloading Bitcoin Core. You don't need to sync 600 GB just to extract your private keys, and you don't even need to sync that much for old addresses to show up in Bitcoin Core.
I'm having the same issue of the poster is having. I bought some Bitcoin a few years ago and forgot my login credentials and forgot the email address that I used and forgot which site I even used but I was able to find the file on my computer after remembering that they made me save a file on my computer before I could see my seed phrase however I can't find my seed phrase either.
That sounds like Blockchain.info. Start by reading
https://bitcointalk.org/index.php?topic=4959742.0.
Doesn't that file that we saved on our computers have all that information?
Who's "we"? I don't know what you saved.
And is there someone that we can entrust our ZIP drives to that can sync them to the Bitcoin core to help us put them in a wallet we can use?
Yes, those people exist. The problem is: you'll only know whether or not you can trust them
after you risk your funds.