If you have a regulator without any provision for absorbing heat, that regulator is probably not intended to be used with input of liquid propane to start with. Regulators that lack vaporizer capability are intended to be used with very low fuel consumption applications (usually less than 8 horsepower) and are plumbed from a tank configured to deliver propane vapor only.
I am getting a visual on this and I think your term "rich condition" is surely an understatement.
A J-model Impco regulator/vaporizer plumbed into the engine coolant (properly plumbed, of course) should give you dependable performance.