But you cannot book until DVLA have accepted your application and approved the medical.
In some cases, reported on here, people have told DVLA that they have found a doctor, only for them to refuse to allow them to use that doctor. They are left then with going through the DVLA complaints procedure that adds even more to the timescales.
Generally speaking, if someone drinks within the guidelines (14 units, spread out over the week) then the CDT score should be acceptable after 3-5 weeks.
The only reason I am hesitant in saying you should follow those guidelines is that you say that you binge Drink. Can you really stick to 14 units spread out over a week, or will one or two drinks lead to many more?
Also a binge in isolation can raise CDT for up to a couple of weeks.
All in all, you LIKE a drink, you NEED your licence back so prioritise the licence application.