Sam, my apologies if ths sounds a little harsh but this type of query is quite common on this forum.
The short answer is, Yes. You need to have certified practical experience and hand skills. If you want a Licence you shoud confirm the requirements with your local authority.
While no-one doubts your academic qualifications, and recognising that you may have some skills through working on school or other aircraft, the AML is based upon proven knowledge and demonstrations of practical hand skills being recorded in a specified manner having reached a specified standard. And the regulation, as you quite rightly point out, requires you to have proof of practical skills experience across the ATA Chapter set over the required duration.
The duration is as important as the skills, ensuring that the applicant is suitably experienced in maintenance routines and practices on 'operating' aircraft.
The practicalities of working on aircraft in a consistant manner and the documentation requirements of differing organisations is quite different from manageing systems reliability and maintainability, cost and finance.
A BEng will help you understand that an aircraft and its systems are airworthy, or not, but you still need a Licence to legally certify it as airworthy and the Licence, through lessons learned, is still a mix of theoretical and practical qualifications including a wide variety of hand skills and practices.
Best of luck if you decide to go ahead.