You can sometimes reduce the steeping time for some flavours by frothing the juice.You can buy a Milk Frother cheaply,or make your own from a Dremel-type hobby drill(I did)and a small brush.That was a bottle of Afro-Dizziac that was burning my throat straight after mixing,so frothed it up & was able to use it straight after mixing.It still improved further over time,just rarely a juice gets any time as I'm too stupid/lazy to mix up a few days supply.
Once I have done it the "correct" method. I can then learn how it should taste so trying the hot water bowl trick and Xbox Trick (and now your trick) I will have something to compare it to to truly find out if it speeds it up or makes it different.