You need to leave a good air space in the container so that it mixes well when you shake it and also turn it upside down as you shake it so that the sugar all comes off the bottom.
After further testing, I'm being won over to this method.
I tested it with a small amount (100 ml) in a plastic bottle, and got a good result after just one day (99% of the sugar dissolved after about 5 shakes). This was a small amount, so I tested a larger amount (200 ml) to see if I could get better results with short bursts of an electric whisk/blender (20 seconds every 10 minutes), instead of shaking, but in the end I had to conclude that shaking works ten times better than stirring. Even with shaking, you never get all the sugar dissolved on the first day, but you can get rid of up to 99% of it).
Today I tried an even larger amount in a 2 litre soft drink bottle (600 g sugar + 300 ml water). Yes, the air space is very important. After shaking, the sugar settles in a tight pile at the bottom of the container, and it takes quite a bit of sloshing to dislodge it, but then you can give it a quick shake and that's that. One shake session every half an hour for about 2-3 hours dissolved about 95% of the sugar. This is more shaking than JEP uses, but I want to dissolve *everything* (or nearly everything).
This evening I took the plunge and filled my nearly-transparent empty 14 litre apifeed jerry can with 6 kg of sugar and 3 litres of water. I've shaken it about 5 times over the course of the evening, and I'm down to about 20% sugar remaining. I have high hopes for the morning.
The neat thing about this method is that it is virtually stickiness-free. I can put the jerry can anywhere in the house (I work from home) where the eye catches it and give it a good slosh whenever I walk past it for a tea break.
I don't use contact feeders so a bit of sugar failing to dissolve is not a problem for me.
I use what is probably known over there as an Ashford feeder on two of my hives, and home-made floatation feeders on my other four hives, so a bit of undissolved sugar shouldn't be a problem, now that I think about it. Still, it'd be nice to get *nice* syrup.