Have no false hope. Have no false despair. Have faith in the process. Ultimately your W has to have a change of heart. Typically, this does not happen over night. Focus on you and making positive changes to your behavior and how you interact with her.
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How do I encourage her to think positively about our relationship and me?
You don't. You validate how she feels. Expressing your beliefs and feelings do not help, but rather hurt your relationship. Trying to control her does not help either.
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Can negative thinking/anger be a good thing?
Any emotional response from her is a good thing. How you react (or rather do not react) is key. You find your happiness. You do not shift your emotional state based off of other peoples emotional state.
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She grabs every niggle and adds it to her 'evidence' list. Everything I do is wrong or misinterpreted. Should I try to explain these to her, or keep away and avoid anything that sounds like justification?
You just validate how she feels. Memorize the validation thread. Another Stander is very wise in the ways of validating.
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We have had several good periods where we have been intimate again. For me these are doubly-good because as well as the physical joy, I can give my love and feel loved this way. Is it ever a good idea for me to try initiating with my wife? (I have to leave it 100% up to her, right?)
Ultimately you do what works. Stop doing what doesn't work. What works for me. I initiate. If rejected, I do not take it personally. I focus on being attractive and seductive and wait for her to initiate.
"What is best for my kids is best for me" Amor Fati Link to quotes: https://www.divorcebusting.com/forums/ubbthreads.php?ubb=showflat&Number=2879712