I can't offer experience with this type of annealing. But, it seems that the annealing EFFECT that you are looking for is not occurring at the temperature that you are using. So, you will need to use either a higher temperature or a longer time at the current temperature. But, longer time is not really feasible, because it is hard to HOLD the temperature with the setup you (and most of us) use.
I suggest that you use progressively higher temperature Tempilaq until you get the effect that you are looking for. I also suggest that you drop the cases into water so that there is no chance that the lower part of the case will get annealed AFTER the case is dropped onto a towel, due to conduction of the heat down the case.
You can get temperature indicating liquids and crayons that come in 50°F temperature increments here: http://www.mcmaster.com/#temperature...sticks/=iz2hj1
and other places as well.
Let us know what actually works.