while i agree that Stevie's sound / droning voice / possible lack of emotion is evident on SYW, i'm not quite sure whether that's a result of too much or too little Lindsey's influence.
just on the bases of watching that Destiny Rules document - he seemed to have been more interested in mending the fences / repairing a relationship and letting her feel his support, unlike during their younger heyday. during Rumours / Tusk / Mirage / Tango years he was not afraid - and probably really enjoyed - telling her what exactly is wrong with her songs and how they should sound. during SYW and more recent times, as you said, he doesn't have all that love/hate emotional investment in her anymore, he's more interested in repairing the relationship, so he is more interested in letting her run with whatever she wants to do with the songs. which results in less of his influence and less of his vision for her songs.
remember in Tusk doc when they are working on Angel and he says "IF we even use your melody" or something like that? i can never imagine him saying something like that these days. and she would never let him, either. so SYW Stevie songs may be a result of too little Lindsey influence and his holding back to tell her exactly what he thinks of her songs.
all speculation, same as yours. but that's my impression from that Destiny Rules doc.
also quite possibly, she is not nearly as open to let her emotions and guards down anymore, like she was when she was young, drunk, and high - especially around someone like Lindsey whose shadow and influence on her success she seemed to have been trying to get out of most of her musical career.
which all leads me to agree with you - while Lindsey and the rest of the band should work with Stevie on her songs (if she has any) and make sure there is a cohesive sound to the album, there should be also another producer brought in, who will not have the same baggage Lindsey has with Stevie, and can say whatever he/she thinks.