I have build a pair of rectangular coils in an Indulgence MT tank, so arranged where the coil was vertical above the air intake towers and externally wicked. The air stream shot through the center of the coil unimpeded. I chose the rectangular shape as this was the shape of the intake ports. It was a beast, frankly, and vaped like a dream. I never repeated the experiment, however, as the MT was famous for leaking like a fire hose if it was not perfectly wicked, and the external wicking required was a chore in that tank.
Unfortunately, I fear you are misinformed regarding "greater surface area" with a rectangular coil unless you are using an atty with such a cramped deck you can fit more wire in with a rectangular pattern than a round one. For any given wire (material, gauge and construction) and presuming an equal number of wraps, the surface area of a rectangular coil is identical to the surface area of a round coil with a diameter of 2 * sqrt{(H*W)/π} where H and W are the height and width of the rectangle in any units of measure you like, with the diameter given in the same units. If the math confuses you, take the area of the rectangle. Assume a circle of identical area; solve for the radius by taking the square root of the area divided by Pi; then multiply by 2 for the diameter. This is true because both coils will contain the exact same length of the same wire (ignoring the legs), and therefore having the same surface area. Another way of looking at it is: build your rectangular coil, then shove a conical probe down the center to undo all your hard work and "round" the coil out. It will still have the exact same amount of wire and the same surface.
But don't let my cussed nitpickiness disturb you. By all means, build all the rectangular coils you like and enjoy. If you will arrange them like a chimney above the intake ports and wick them outside the wraps, they'll steam like mad and the vape will be a bit hotter than you will be used to from a center wicked coil of the same build. And, I suppose, I should also mention if you happen to have an atty with a circular (or oval or triangular or etc.) ports, building a coil in that shape and arranging the air flow through the center will offer similar performance.
Edit: Back to the math. The ratio of circumference (or perimeter) to area with a rectangle is greater than that of a circle, yes. But all that means is it takes more cotton to fill the coil, not that you're getting any more in contact with the wire. Still, perhaps there is some benefit there, especially at very high watts, as there will be more juiced wick close to the wire with a rectangle. That might make a noticeable difference by having a greater "reservoir" right handy to the heat where it's needed. But if so, you're skating pretty close to the wick's ability to transport juice and risking a dry hit on every puff.
I tried a few times to make one pretty but really couldn't. Kept deforming on me. Probably shoulda used lower gauge and not wrapped in parallel. After watching the vid, I really see why. Never annealed the thing. Now I gotta get a torch.
