Is it possible to link the public key for every bitcoin address in your database?
If I can get the data I can add it. I'm no expert on this, can I use anything from
inputs (maybe spending_signature_hex?) to get this data?
I looked for compressed keys at the end of the spending_signautre_hex values and I found that a lot of them don't have public keys at the end. Makes me think they are signatures of transactions, not scripts.
So the real solution (fell asleep while studying the dataset

) is to take the transaction_hex field and pass it as the argument to the "decoderawtransaction" RPC call. It'll return JSON where the signature script is located at [N]["vin"]["scriptSig"]["hex"] for each input index N and then get the compressed public key in the last 33 bytes of the hex.
You'll obviously need a bitcoind for that and it's possible to configure access from another machine if you're resource-constrained on the box you're parsing this address data on.
I think bitcoind should be able to handle the load, especially if it's running locally.