Sorry Andrew that I hadn't seen this when you posted it -- just found it reading up on foundry posts, as I hope to start casting again soon. Your original question was never answered, so here goes just my own experience with my waste oil burner.
The setup:
4" thick firebrick lining
chamber, about 7" diameter
homemade atomizing burner
time to melt an A6 crucible of cast iron scrap, about 1-1/2 hrs (from cold)
fuel, diesel with or without about 10% used motor oil
fuel consumed per melt, about 1-3/4 gallons (US measure) (from cold)
So say about 1.4 gallons/hr
Say 130,000 Btu/gal (US)
Fuel heat input = 182,000 Btu/hr
or 54 kW (fuel input)
You can make adjustments for efficiency of burner(s), burner actual power vs fuel potential , and efficiency of your planned furnace construction - and its size compared to mine, but at least you have a data point here.