Sounds like we have a similar method. I have the Roe vented upper hose, which BTW is far from a miracle. Does however make it easier than that pipe plug on the stat housing.
Anyway, what I have done several times:
Fill system with vent fitting open, using my funnel that fits the coolant bottle. Nothing ever comes out the vent hole during this process.
Close vent, and with fluid in the funnel covered with a towel, start car for 30 seconds to a minute. Fluid level in funnel will rise due to the air heating in the engine, and then fall again as the air cools. Check vent to see whassup there.
Allow to heat soak for 15 to 30 minutes.
Repeat process until stat opens. This takes 3 to 4 hours. I have the time. If you don't, then I would of course find an alternate method!
When stat is open fill system to as much as it will take, checking hose vent. Close system, ensuring fascia bottle has fluid and the hose between the 2 has no leaks. You can otherwise **** air as the system cools.
From there, with driving in between, I've maybe seen the level in the fascia bottle drop about 1/2" or so, as the final air works out of the system.
No cooling problems in Texas.