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Won't do it safely
Just for another viewpoint, I own and regularly fly a 1973 P337 with 123 gallon tanks. Your calculations seem to have forgotton wind, reserve for taxi, runup and climb, potentially unusable fuel, and reserves. I flightplan 10 gals for climb to 16,000, and 25 gph for cruise. This is a bit too much, but seems to work out within a few gallons. Therefore, the fuel exhaustion time for my airplane is approximately 4 hours and 45 minutes from takeoff. I run at 65% power approximately 65 degrees rich of peak on the first cylinder to peak. I will in fact get a TAS of 190 kts at 16,000, but headwinds more often than not reduce this, such that I use 170 kts as a flight plan groundspeed. I try to land with 60 minutes of fuel left, therefore my max range is 3:45 at 170 kts, or in other words, 637 nm.
With no reserve fuel at all, I calculate the range for my airplane to be 807 miles, assuming a 170 kt groundspeed.
You might barely be able to make such a trip at a very low power setting, perhaps 45% power. You'd still have a 140 kt groundspeed in that 20 kt headwind, and you'd land with a bit over 30 minutes fuel. I can't vouch for this, I have never run the airplane at such a power setting.
If you need 800nm range, buy a later model Skymaster - a H model, with the 148 gallon tanks. I wish I had them.
Kevin
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