The fact of the matter is airlines offer the courses/apprenticeships to gain B licensed engineers. With this qualification and type-ratings you can legally work on aircraft. Airlines want B licensed engineers, there is no other route in and there is nothing wrong with the 3 year B licensed route otherwise what's the point in airlines offering it and spending all the money on training people?
I'll try again.
The point I am trying to make is that you are dismissing the apprenticeship that does not necessarily get you a 'B' without considering what it will get you.
By the way you do not need a licence to legally work on a/c.
Aircraft mechanics do the work whether they are 'A' licensed or not. If they have the 'A' licence plus appropriate type training then they can cerify some of their own work.
A 'B' licence plus appropriate type training means you can certify other people's work.
Apply for the lot but if the only offer you get is the apprenticeship that 'may' get you an 'A' Licence then grab it with both hands.