"Wouldn’t adding fuel to an already fuel rich mix make a carburizing flame instead of more heat? Correct me if I am wrong here, as I’ve never had to deal with high altitude forging. "

If you really are fuel rich to the point of using all oxygen then yes. However you may actually be fuel poor (oxidizing flame) and think you are fuel poor, something I've seen even at sea level. Most people remember from high school science that hydrocarbons burn to give water and CO2 but that is very simplistic. A reducing flame produces CO and CO2, and results from having more fuel then oxygen but not so much as to have a sooty flame. Reducing flames are hot, hotter in fact then most fuel poor flames.

The right mix of fuel to oxygen, omitting reactions were nitrogen is converted to NOs is between these two chemical equations:

CnH(2n+2) + (n+0.5)O2 -> (n+1)H2O + nCO

CnH(2n+2) + ((3n+1)/2) -> (n+1)H2O + nCO2

where n is the number of carbon in your fuel (these formula don't work for unsaturated hydrocarbons, like acetylene), For propane, n=3, so
you need between 3.5 and 5 moles of oxygen per mole of propane. This works out to be about 17.5 to 25 volumes of air per volume of propane at room temperature and 1 atmosphere of pressure. There are tools to measure gas flow rates and with PV=nRT one can correct for higher pressures, so this isn't an impossible way to approach the problem.

If you are within the right fuel air mixture ranges, then you fuel mix isn't your problem and it is time to look at your forge design. Consider issues like: cold spot due to poor gas flow through the forge, to few burners for the size of the forge and are the burners to far above/below the metal you are trying to heat.