New pickup suggestions...

I use a JB/Jazz set in my CE24. It sounds great, both clean and dirty. I use a Friendman BE100 patch on my Kemper for 90% of my tones and I get a nice mix of a 80s metal and modern hard rock tones.
 
I recently had trouble dialing in my hbii with 58/15 LT's and was getting frustrated. I ultimately put in some dragon ii's and couldn't be happier. They sound amazing and it really opened up the sound. I know a lot of people knock the dragon ii's but I love them. They seem to cover all of the tonal ground you mention in the op. They are a little hotter than the 85/15's but don't venture into metal guitar territory or anything.
 
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