there's always post quantum rsa https://eprint.iacr.org/2017/351.pdf. yes it sucks, but at least for the quantum computers we're likely to have 20 years from now, you could probably get away with a 1gb key...
Lamport signatures work and are PQC. There are solutions that are practical to use (1gb rsa keys are not). Just not drop in replacements without large tradeoffs.