In my personal opinion, the setup would be better reversed...
Air is less restrictive than liquid, and liquid requires more surface-area contact for effective vaporization. EG, a thin pencil-wick will empty faster than it fills, and will empty fast. As opposed to a tube-wick which will refill faster, have more surface contact with the element, and allow for adequate cooling air-flow to release the vapor.
In short, what all that above says...
Pull out the wick from the center of the coil.
Wrap a thin/thick fiberglass mesh around the outside of the coil.
This allows adequate steam/air in the location of the old wick, while the new outer wick holds enough liquid for a longer puff, and can refill faster from the unrestricted flow. (The flow of a wick pushed inside the coil is less as it fills and steams. The restriction of the coil on the wick, added to the expanding wick with the liquid, restricts too much, allowing the element to overheat, burning the wick.)
I am not sure if they use fiberglass in the wick or some other foreign high-temp plastic. Both will burn at high temps, but thick-strand fiberglass is more heat resistant and will hold more liquid if it is placed around the element like a sock/tube. (Water only gets up to 100C then it instantly vaporizes which takes the heat with it. You need high pressure to get water above 100C. For all basic purposes, it will/can get hotter, but this is not a debate about large-volumes of water and pressure. This is about a micro-drop in a negative pressure environment while you suck and it heats-up to boiling temps.)
One day, I hope to see a pyrex contained heating element. Since glass is non-reactive, but metals are corrosively reactive when heat and oxygen and acids are applied.
Having the element inside a pyrex glass blister will also stop burn-out, corrosion, allow you to clean the element without harm, and allow the entire circuit and battery area to be separated. (Thus, no lithium gasses being sucked-in, in the event of battery failure.)
They could also switch to a stove-top curled heating element, and use a standard flush-mount disk-wick, with a needle-insert into a full liquid cartridge.
NOTE: You should be able to have a full liquid cartridge with a fiberglass wick and end-cap. The wick will draw liquid up to the pad, and the pad will contain enough to puff. Think of the wick as a thumb-tack shape, with the pointed barb inside the liquid like a straw, while the flat side rests against the coil or wool.
Even better...
Drop the whole battery and heater-coil... Replace it with an air-brush style setup. Use the suction of air across a "T" connection. Essentially acting as an air-brush. Drawing up liquid through a thin tube/wick, and diffusing it through the air-passage of the faster moving air being drawn inside. (On the reverse, a mini-pump-bulb could create enough pressure to power the cig with atomization for several puffs. The atomized air would be in addition to the air being drawn-into the chamber, not the source of all inhaled air. Essentially like an old perfume spraying bottle, but smaller.)
Go super-low-tech...
Strip all the innards, and fill it with a wick and a tiny straw. Put a bunch of holes in the straw and just suck. Refill as desired, gut it out when it no longer works. (Not sure how effective that would be, but I have done something similar for a terrarium humidifier. Nicotine is highly evaporative and easily becomes airborne. Only the glycerin requires high heat to create smoke-like looks.)
You can also extend the life of the battery and the coil, with a reduction in smoke, but no loss of nicotine, if you add an in-line resistor to the coil. (That requires disassembly, and is not for those who do not know about electronics.)
You can also over-drive the coil, which will shorten the life. By shorting the length of the coil. Resistance is equal to the length of resistive wire in the device. Shorter coil equals less resistance, equals more heat, equals faster battery drain.
