Luci, I haven’t listened to your recording but will do so immediately after writing this.
Why do the accents sometimes change? Because we stress words in different ways to convey different meanings. You could equally ask why the same word in a different place or sentence has no pitch accent. These are pitch accents, remember, and typically used for emphasis in a communicative context, rather than in the predictable context of enunciating single-words only.
Is there ever a grave accent placed upon a stressed syllable? I don’t believe that will be likely.
Look again at Lily’s rules and note that stressed syllables can receive a grave stress: fuèrunt, penultimate long by nature, ultimate long by position (in the category of ‘other cases’). I think this is very revealing, because we do pronounce the word this way. It helps to establish that the rules are descriptive before being prescriptive.
I’d be happy to call stress ictus but what’s wrong with just being rigorous about talking about stress and pitch to distinguish these types of accent. I think that might be better because, there’s a strong possibility that the stressed syllable (normally understood as the accented syllable) is retained in an adverb such as ‘sane’ (the first syllable) while receiving a drop in pitch accent on the final syllable. Although, it would be much more interesting if that were not the case.