The key for me seems to be full sun. They mostly only flower in the tops of the trees. So they have to be 3 to 4 years in the ground, minimum. Even then, only the parts of the pant getting full sun will flower.
Mine flower in winter. December and January. That makes it tougher if you're growing in a pot that you bring in for cold snaps. If you can't grow in ground, I'd suggest the huge pot, like worked for abraxxas.
For my money, I'd go get a big thick heavy duty trash can or a plastic shipping barrel. Drop a full 8 foot 4x4 fence post in there, dead center in your container, with a strip of lattice or something else tacked to the exposed top of the post so the young searching tendrils will have something to grip onto. Fill the bottom foot or so with rock to weight it down and help the bottom drain. Then fill up the rest with soil and plant your vine half a foot from the post.
Once established, put it in full sun and water it like crazy. Only bring it in for actual freeze events. For 33F it's not worth the shock of changing it's light habit. Don't try this method if you don't own a dolly (hand truck) to move the pot. Prune and train it how you like on the post/lattice. You can get some fat vines but also keep some one-year and two-year growth around at all times especially near the top. The most flowers come from pencil thick, just woody vine portions that are in the first year of woody growth, so their second total year of growth. Once a section gets too thick and barky, it won't make flowers, preferring instead to make new shoots.
Another item of note, it's possible the flowering season for caapi may be more related to rain patterns than sun. Where I live the caapi flower in winter which is our dry season. It may be that they like to flower in summer where that is the dry season? Just a thought.