I don’t think I can keep up with you…your FAST! LOL
I am enjoying your enthusiasm for your sea kayaking discoveries. Makes me smile. I find joy in the boat handling and will weave my kayak in and out of the overhanging branches that drupe into the water along a deep shoreline of lakes and slow rivers using edging and paddle strokes that are not used as often in open water. A paddling friend called me Woody for doing so.
Outside edge (into flowing current) is a fundamental move for kayak playboaters. The bow or stern edge dives into the current and loads the kayak for the next dynamic move.
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Like you I have made the transition from a canoe to a kayak recently, although for a different reason: my canoe became too big for me to paddle comfortably (or I became too old 
But anyway, the confusion about heeling, or edging as the British called it, stems from the fact that it is usually not explained very well.
The effect you get when you heel your canoe, depends on:
When you heel to the right when moving forward, the resultant asymmetrical shape of the hull in the water will give the canoe a tendency (Bernoulli effect?) to move to the right and vice versa. Because the bow normally has more resistance than the stern when moving forward, the stern moves stronger to the right than the bow with a resultant move to the left, assuming normal trim (even keel) and movement straight forward.
For regular touring canoes with normal trim the effect will be marginal, especially with a heel less than 10 degrees.
Some designs may do this the opposite way, but these are not the hull shapes one is likely to find in the regular touring boat.
So it only works when you have decent speed forward and how much it works also depends on the hull shape. Some designs will noticably enhance the turn, others not so much. (Personally I favor neutral behaviour, because this behaviour can also manifest itself for example when paddling in waves when you don’t want it.)
Heeling to the outside of turn is less stable however, so it depends on the situation what is more important to you on that moment.
On moving water stability is often more important and the boats used are usually maneuverable enough…
You probably won’t have much trouble edging the correct way after some practice, because short WW kayaks (probably canoes, too) just feel better edging toward the inside, while long sea kayaks usually turn better edging on the outside. That assumes the sea kayak is on fairly flat water. Some sea kayaks will turn edging to the curve’s inside, even in flat water. Mine did, but unless in moving water, they turned more quickly by edging to the outside. This is more pronounced when turning into the wind.
It helps in both situations to initiate the turn (from a forward-moving start) by first looking in the direction you want to turn while edging and THEN doing the sweep stroke.
To avoid wrong-edge oopses, my mantra was always “Moon the current.” In either the WW kayak or the sea kayak. And I learned to get comfortable and quick at switching edges, which no doubt you already know about.
I started paddling with sea kayaks and only years later got a WW kayak and practiced in a play park. Edging the wrong way from “using the other boat” more was never a problem. They just feel so different from each other.
First to make sure we are all on the same wording - edging toward is the side you are kind of leaning toward (though I don’t like that word, as edging and leaning are different actions in kayaking). Edging away is the side you are pointing you butt to - the side you are lifting your butt and thigh on.
In general with most strokes/moves, you edge toward the side that your paddle is on or near the water with. This is because the side you are edging toward is the side you are more likely to flip on, so having the blade in or close to the water on that side means the blade is in the better position to do a brace.
The two main exceptions to this that I can think of are bow rudder and cross bow rudder strokes.
If you are paddling forward and start an edge without a stroke to start a turn, you should slowly turn toward the side you are edging away from. That said, if you took a forward stroke just as you started the edge, the turning moment from the stroke can overpower the turn moment created by edging, so if your last stroke was on the side you are edging away from, you might turn the opposite way you’d expect. Just something to watch for as you play around.
This makes sense - so when you do a forward sweep you edge away from the turn. When you do a reverse sweep you edge toward the turn. When edging for minor corrections when paddling forward, you edge away from the direction that you want to turn (unless you are crossing an eddy line into current - then you edge toward the turn).
I did find that sometime you need to initiate the turn or the forward momentum would overpower the edge - stern pry seemed to be the easiest. Lots to practice.
If I do that with my canoe, the next “dynamic move” is a swim 
If you want to bring the bow around in a turn more quickly, I find a bow rudder (static bow draw) on the side you want to turn toward can do that. It can really bring the bow around. You do need forward momentum (the more the faster the turn). You want to do it with less of an angle to the bow rather than more because increasing the angle acts as a break to forward motion.
When you raise the hull on the side you wish to turn toward it puts the other side of the hull deeper, it is the curve of the hull matching the direction of the turn that provides a benefit. It becomes a curved keel so to speak and helps to reduce the depth of the ends as if the kayak now has more rocker.
I try to keep my torso vertical, trying “not to lean” my body but push down with my offside hip and raise my onside knee.
A good exercise for edging is backwards figure 8s. We did that in 2 star and it was near impossible to do them (unless you’re talking about a football field sized figure 8) without edging.
I need to get the forward figure 8s down first. Backwards figure 8s - yikes, but maybe not too bad with back sweeps.
I think, reference canoes, that edging depends upon the subtle shape of the boat. A flat bottom Grumman (18’), only barely edged. A slightly rounded bottom Clipper McKenzie (20), easy to turn. On long trips I normally switch paddle, saves kilo-calories. If I edge a bit 5 or more strokes before I switch, not a problem. In white water, edging is just a normal and required practice. A 20 foot boat may have just 21 feet to the next rock and edging can accomplish two things. maybe three? Edge to quicken the turn. Edge to lessen the width of the boat going between rocks. And edge to effectively give yourself a canoe with 18 inches of rocker. That 'get a cheek down deep in the water is the essence of freestyle canoe handling. I AM too old, and too fat to get back into the boat. That is what river banks are made for.