My preferred method consists of hot water bath for about 20 minutes immediately after adding all the ingredients to thin the mix, then a rigorous shake. After shaking, I take the tops off to let them breathe and put my bottles in an ultra sonic jewelry cleaner for about an hour. After that they go right into a cabinet for about a week to two weeks depending on the flavors with a rigorous shake once a day. This method, I feel, works great. It really doesn't speed anything up, but it's the best way to homogenize if you don't want to buy or build a magnetic stirring device. I use a crockpot set on the keep warm setting for heating, and you can pick up a jewelry cleaner at Walmart in the jewelry section for about $25.
FWIW this is the method I use to get a good balance of quick turn around and juice that doesn't loose it's flavour too quickly.
I make up the recipe and give it a quick shake. I put the juice on a heat pad (bottles capped) and warm it to about 35-40C/95-104F - it takes about an hour to heat up to this temp and doesn't get any hotter. About an hour after they're put on the heat pad I uncap the bottles and squeeze out the air from the head space and then give it a thorough shake. Bottles back on the pad for another hour and repeat the squeeze and shake. Remove from the heat pad and into a dark and cool drawer.
Most recipes seem good to go the next day and peak in flavour at about 1 week. They stay pretty good until week 3-4 when the flavour starts to drop off.
I like to mix and vape pretty quickly and I don't like having lots of juice around so this method has been working well for me.