NAPA sells a "Safe-T-Stat." I don't remember the brand name they use but no matter that. These T'stats have a very short lifespan, essentially until the stat opens fully, then it's over. Time for a new one. There are a couple of little hooks that grab onto the movable part once fully open and won't let it close again.
On a hard pull the stat will fully open rather soon and when you go over the top and watch the gauge on the way down, you'll see the temperature drop to around 140 on an 80 deg. day. Then it's time for a new stat because it will never close. 2-ton trucks with 261s have bigger radiators but it's still not enough for long mountain grades in hot weather. Remember these trucks came with an 85 HP 216, not a 150 HP 261. There were only so many square inches available within the sheet metal design so they made the radiators thicker but at some point you really need more square inches. GM did that post ''55 and you'll notice from the truck spec books that the 2 tons with 261 I6 had larger radiators than the 283 V8s.
Another interesting factoid is that the temperature where the gauge sensor is, between #5 and #6 cylinder, will be lower than at the thermostat housing. I've checked. When the gauge pegs on hot (GMC one reads 220), the sensor I added in the t'stat housing reads about 235. This is on a low-waterpump 235. Same for the 261. The part that the OP cut off the NAPA170562 is the valve that allows internal recirculation with the thermostat closed on the later engines. Without that feature, as soon as you start up a hill and the engine starts producing heat, some spots in the engine will boil the coolant before the t'stat can open. Not good. Many 261 truck engines had such a setup but that replacement part number is NLA, so they've nearly all been changed out for the 235 design.
The secret to cooling under load is to flow as much water as possible, which will reduce the tendency to form hot spots that boil water locally in places in the system. AC equipped GM V8s came with slightly smaller water pump pulleys spinning the pump and fan faster. To maintain temperature under light load, add a restriction to water flow, air flow or both. Back in the day before fast-acting thermostats, heavy trucks had shutters in front of the radiator that closed as soon as you topped the hill. You could hear the pitch of the fan change when they closed. This was also before the days of de-clutching fans. On some routes the shops would remove the fans altogether in winter to save fuel; not on I-5 from Seattle to LA but on the Seattle to Chicago route or Seattle to Edmonton.
