This seems like an awfully fuzzy thing to try to delineate. I'm going to claim that the answer to your question is "you classify an AMV as an ASMV whenever you think that sounds like the right thing to do".
See, the thing is, "ASMV" is strictly a piece of fandom jargon that sees no use outside a small sub-subcommunity of the subcommunity of AMV creators. As such, there is no authoritative prescriptive definition of this term that we can use to answer your question.
Since we cannot hope for a prescriptive answer to your question, we must instead turn to a descriptive approach - the question we now seek to answer is "what do people who use the term 'ASMV' typically mean when they use it?" rather than "what ― in some absolute sense ― does 'ASMV' mean?".
However, this question is also nigh-unanswerable. Despite this phrase seemingly having a transparent and compositional meaning (unlike, say, "floogleglorp"), people who discuss this term do not seem to arrive at a consensus about what it means. As evidence, I present this 2013 thread from AMV.org, where a number of people involved in the creation of AMVs are unable to agree on what the term means (or should mean). I can hardly find any other good discussions of the term (or even of "ASMVs" s a concept); I think that this strongly suggests that there is not a shared understanding of what is meant by the term "ASMV".
Given that we cannot identify a definition for this term, it surely is not possible to answer questions about nuanced things like "Do [speeches] have to underlay the very majority of the whole AMV or is it ok if they underlay only 1/4th of it?". Hence, you may as well use "ASMV" to mean whatever you want it to, provided that it still has some relation to the compositional meaning "an anime music video that in some way involves a story". Perhaps other speakers will coalesce around your conception of what exactly constitutes an "ASMV".
(But ― personal opinion here ― I doubt this term will ever see increased use, since it does not really serve any purpose, at least not that I can see. AMVs that tell a somewhat coherent story have been around since time immemorial, and people have gotten by just fine without a discrete term for them, which suggests to me that this neologism is unlikely to be taken up by people.)
Side note: the earliest attestation I find for "ASMV" is this YouTube video from 2011.