I didn't read the entire thread, but I have to go with Metal God on this one...
Throwing metal chips for 40+ years, doing a bunch of heat treating, I can tell you there is no way to anneal copper or brass without an accurate temp indicator.
The best thing I can tell you is if you insist on using 'Gas' then you MUST have an accurate way to tell the temp of the BASE MATERAL,
NOT the surface you are laying heat to!
Temp paint on the outside is worthless, the gas will cook it.
Temp paint on the INSIDE of the case will give you a pretty good idea,
But not 100% accurate.
Keep the flame at an 'UP' angle towards the neck/shoulder so flame doesn't contact the temp paint or your readings won't be accurate.
The one thing I can tell you is,
*IF* you see the 'Puff' of smoke from the case neck, the case is ruined for all practical purposes.
That smoke 'Puff' is alloy compounds reaching combustion/vapor point.
See the 'Puff' just throw that case in the 'Plinking' brass pile, its not going to be accurate or live long...
(I found this out the hard way!)
Personally, I've gone to electrical induction heating and a timer...
12 to 24 volts, $50 worth of parts, a $20 infrared pyrometer and you are off to the races.
'YouTube' is full of home made induction coil heaters,
There are $50 parts kits sold a lot of places,
A 555 or 556 timer IC from Radio Shack so you can control EXACTLY how hot the case gets...
Once you hit your temp mark its 100% repeat-ability.
Commercial units run anywhere from $250 to $500 for basic to $1,500 for advanced units.
Homemade under $50.
This is the controls I built for my commercial production unit,
About $300 in parts, running both timers & infrared for redundancy.
Spits out 6 cases about every 2.5 seconds.