HX1200 is strong enough to run all 4 GPUs, even in a peak condition of 170w each one
Call you tell which connectors are melted?
It's not rare to people use sata cable to power risers and them the cable melts, this could be a big problem and led to bigger issues.
Check here:
https://cryptoage.com/en/1580-why-the-serial-ata-power-connector-sata-is-so-dangerous-for-assembling-mining-rigs.htmlIn my opinion you need to verify the cause of this first
No need to replace all the risers, only the fault one
To run the setup I would pick a 850w gold PSU, Corsair, EVGA, Seasonic, XPG etc
I'll say again, check everything because melted cables can lead to something worse like a fire