Just chew nicotine gum, sheesh! These kids and their vapes..
Anyway, you're right, nicotine is a pain to quit and I wouldn't recommend it obviously. But vaping seems to be even more unhealthy and more distracting.
Nicotine gum is as expensive as cigarettes, if not more. I spend about $30/year for my vape supplies. I buy juice by the liter and the coils are the only other consumable and those are about $2 apiece every few months.
I mix my own juice. I did the math a few months ago, and I can make 60ml of juice (which lasts me about a week) for about $1.50. Coils usually last me about a month to a month and a half, and I usually pay $5ish a piece. So yeah... my monthly vaping costs are about $11/month at the most.
So, doing the math, as I use 3mg/ml juice, I vape about 720 mg of nicotine a month. If I bought the cheapest Wal-mart generic brand gum, in the 2mg pieces (because to replace my vape, I'd want a low dose per piece), 720 mg of nicotine in gum form would cost $81/month.
That is a huge difference. Even accounting for the fact that my vape device cost me originally $70, it's still cheaper, potentially as soon as the first month, to vape over chewing gum.
Coating regular gum would probably not work. The nicotine is embedded in the gum base itself. That's why the instructions for using nicotine gum say to chew just long enough for you to feel the tingle that nicotine creates against your oral mucosa, then tuck it between your gum and cheek for 30ish minutes or until the tingling stops. Then you give it another couple chews, just enough to expose more of the nicotine to the surface, and place it between gum and cheek again.
The nicotine is slowly absorbed through the oral mucosa. Coating the gum would give you an initial burst of nicotine, but would not have the sustained drip of nicotine that the traditional nic gum does.
I suppose one could melt down gum base, add a vaping nicotine solution, stir it together, let it set and then cut into pieces... but I would worry about the PG or VG that the nicotine is contained in doing something weird to the gum base. And you would have to be careful to stir it quite thoroughly to prevent nicotine "hot spots" in your gum.
Making a homemade lozenge or mint would be much easier, and I believe some people do, in fact, do just that. It would be similar to making hard candies, only at some point you would mix in the nicotine liquid. Since many of the flavorings used in vape juice were originally designed for use in baking and hard candies (and usually have a PG or sometimes VG base), I'm pretty certain the PG or VG of the nicotine won't screw up the texture of the candy.
I know how to make gum and it would be a hassle and a half for this purpose. I'm fine with unflavored juice composed of compounds that have been used for inhalation purposes for decades.