Hot Fuel Lines

I would regulate the pressure as close to the carburetor as possible with a bypass regulator. That way a lot of gas get recirculated, only what's needed goes to to carb, the rest goes back to the tank. There is absolutely no way the fuel can get hot if you route the gas lines as shown in the below diagram. I had basically the same problem you are having and this solved the problem.
View attachment 1715354497

I've preached that for years right here on this forum and been argued into oblivion, so I've given up. All the naysayers said it doesn't matter where the regulator is. I like mine as you say, as close to the carburetor as possible, but on the return side. That way you're using the regulator as the return restrictor. Of course you must use a return style regulator, but there are plenty out there to choose from. It does make a difference, IMO, where the regulator is. At least it always has for me.