Brief Answer:
Not the way it is done.

Detailed Answer:
First of all, the more successful ways of changing behavior involve others:
behavioral modification (rewards for immediate changes in behavior.. basically like an animal training program; requires ideally an immediate award associated with the behavior; it has been hard to implement outside of experimental or residential environments).
12 step programs
http://changingminds.org/explanations/theories/self-perception.htm
have a firm scientific basis and are analogous to treatments that are so effective they are banned (12 step like programs used as pharmaceutical advertising, cults, etc.).
Those are better than 50/50 effective; more so the more intrusive that they are (12 step programs with intrusive sponsors or directly involving the family are a bit better).
There are medications that are a little bit (25%) helpful.

That being said, the gradual reduction is reasonably good at preventing the mroe serious medical complications of alcohol withdrawal one would see with cold turkey from a large daily dose of alcohol. (1-2 drinks per day is unlikely to produce significant withdrawal).
So... if you are not going to seek (expensive) medical intervention, then cutting gradually daily down to 1 drink a day or less prior to abstinence is safe but generally fails. generally people cannot follow through on this outline for even one week. Cannot say in your particular case

BUT

The most recent advise in all addictions is a combination approach involving the reward aspect and cognitive approach. Try exactly what you are planning. Set up some reward if you succeed at 1 day, 3 day, 5 day, etc. (not involving drinking) Involve others in the reward giving.
Then.... here is the most important part.....
when you fail, learn what occurred in the failure. There are external and internal triggers to drinking. It is hard to know them before they occur. But when they occur you can identify them.
Then...... I advocate the four tiered approach in my book "The Way of the Devil Diet".
First, you could just cold turkey fight it (This is included as a BAD way of doing things).
Then there's avoiding (not having alcohol in the house for a start).
Then there's lieing (actually... it's more substitution... when you see what your triggers are, you can have other non-allcohol things that help it).
Then there's the low transform (you have everyhting just the same as it is but put it into a larger context that changes everything... for example exactly like I said about finding one's triggers, identifying them and setting up rewards about learning/dealing wiht them). You still have the addiction and triggers, you are just having the addiction process teach you how to deal with it. (transform).
Then .... there is the high transform... it's the same as the low transform. It's exactly the same....you just involve other people into it. So....
becomeing a sponsor
helping others
volunteering
sharing at a 12 step program
writing a book
(let's face it; nobody is going to give a better answer than this).

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Brief Answer:
would require actual testing

Detailed Answer:
Stool that has blackish color can have blood in it and alcohol often causes gastrointestinal bleeding.

Requires a simple test (might be over the counter) to tell if there is blood in the stool. this can be a serious condition and the bleeding can rapidly go from slight to severe and life-threatening.

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