That explains the difficulty I had using the brass rivets. That, and maybe incompetence. Anyways.....
Asking the almighty google, it looks like a few seconds with a blow torch should anneal brass pretty quickly. I'll go back and re-read the link you sent to see if you already put details there.
The gun-folks who re-load brass had this info to offer (let me know if that sounds about right):
Brass is annealed by heating it to a certain temperature for a certain amount of time. The higher the annealing temperature, the shorter the time required to anneal. The grain structure of the brass begins to change - indicating the start of annealing - at just under 500 degrees Fahrenheit. At 600 degrees F, brass will anneal in one hour. At 800 degrees F, brass will take only a few seconds to anneal.

Only the case necks should be annealed. If the case body or head is allowed to overheat, the case will be completely and irrevocably ruined for reloading. Also, no portion of the case should ever be allowed to reach 950 degrees F. At this temperature, over-annealing will occur, rendering the brass too soft and weak to reload.

As you can see, annealing is a balancing act - the neck must be heated (but not overheated) to the appropriate temperature for the appropriate time, while ensuring that the rest of the case does not reach a temperature that will cause it to soften as well. In addition, your process needs to be very consistent from case-to-case in order to preserve accuracy.

Cartridge Case Annealing - MassReloading

More about making and setting rivets is at Brooks saddles - modifying the frame/recovering
I anneal after the hammering to size and shape using the anvil, and before the final shaping work using the vice mounted drill.
I place the rivets onto a heatproof sheet and then heat the copper to cherry red with a MAAP gas torch then quench in water.