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?
> block that I own and has been unused since the mid 90's
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.
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.
You don't need to sign an LRSA to use the prefix; there are some legacy holdouts still using their original prefixes without any agreement or fees with ARIN. Signing an LRSA will give you access to ARIN IRR/RPKI/rDNS/etc services, which can be quite useful, though.
I'd recommend creating an IRR route object for your prefix and ASN on AltDB (or finding a sponsor to do so on your behalf). Once you have that in place, you should be able to announce it without issues, without any ARIN involvement. Growing adoption of RPKI filtering may make this increasingly difficult in the future, though.