I am wondering if it is possible to reduce the field to 130 bits or less.
No, that would be woefully unsettling. The security of elliptic curve cryptography extends to half the field size. The 133-bit curve only has 64.5-bit security. That is, ~264.5 Curve operations can calculate the private key for a given public key. This is a very small task for a competent attacker.
Without interfering with actual functionality
Even if it wasn’t a terrible idea, this would be an extremely invasive change that would require the entire ecosystem to adopt and shift to a different, smaller curve. every Bitcoin software must adapt.
As far as I know, there are no recommended standardized curves for sizes less than 160 bits.
What this means is that the actual generation of the secp256k1 public key should not be interrupted.
If this were possible, the Bitcoin ecosystem would have already embraced it. secp256k1 uses a specific finite field, integer modulo. 2256 – 232 – 977. Using different fields will result in a different curve with different private/public keys and everything.