MMmmmmmm, tricky. That's a big range of tones you're after. For the neck, I think I'd be inclined to try either the Holydiver, Crawler or Abraxas. The Holydiver is the most obviously Rock/Metal of the three but is also surprisingly versatile. Still not obviously Bluesy though. The Crawler could be a great option. I have a Crawler is a PRS SE CU24 that doesn't sound that different to the Tremonti acoustically to me. It's not particularly 'tight' but it is a very articulate pickup that will give your Tremonti a very 'Les Paul' tone. It's thick, rich and sweet sounding, does a great Blues Rock tone and will also run into early Metal territory. The Abraxas is similar but a step back from the Crawler.
For the neck I'd investigate the VHII and Black Dog if you want humbuckers but to be honest, if it was me, I think I'd be looking at using a Mississippi Queen for this application.