Is there a way to get a /24 block that I own and has been unused since the mid 90's routed without signing a new contract and paying the new ARIN fees?
It's possible that your block is a part of a legacy allocation, they are governed differently.
This timeline suggests that it's still a legacy allocation. The new governance structure does not apply unless you sign an RSA or LRSA agreement with ARIN.
https://www.arin.net/resources/fees/fee_schedule/#legacy-reg...
So you won't be subject to the new fee structure.
If you want to route then you will need an ASN and an ISP willing to announce them. So long as you are up on your LSRA dues I don't see how you won't be able to utilize them.