Chilling requirements vary by plant. Some need to freeze the tops, others like perennials we have here in FL go dormant as soon as the nights dip below 55. It has to be cold enough to send a growing plant into dormancy (gradually over a week or two, not suddenly like shoving them in the fridge) and keep it there for a month or two. Probably down into the 40's at night and no higher than 55 or 60 during the day. I don't think 4 days in the fridge is going to cut it as 100 hours of chilling.
Hm, where you live, it's a puzzle! Perhaps a big planter on wheels that you could move from the sun to the shade for winter, then water it daily with ice cubes to cool the soil, and maybe insulate around the planter and put a cooler upside down over the top to give the plants a dormant period. Once you've kept it cold for a month or two (however long you have patience for) you'd gradually move it back out to the sun, and when the plants start growing again, water and fertilize.
If you can source the plants now, they will have been dormant. You could grow them over this summer, you might get one crop of berries this year if the plants get big enough in one (long!) season. Then next winter you could worry about getting them to go dormant or just let them do their thing.
It sounds like a lot of work to me. I'd look for somebody who will just import the fruit for you, myself.
