Yes, he does.
The mini-humbucker will help, but they do not pick up as much of the string as a real humbucker. .011's or .012's will help, though the guitar will need to be setup for them. A big pick will also help. The Dunlop Jazz picks are nice, Dunlop purple Tortex picks, or Fender extra-heavy picks are all good choices. I also do not use the pointed end of the pick, but one of the more rounded corners. Even better than a pick is to learn to play with your thumb, ala Wes Montgomery.
The truth is, though, if you want that Wes or Joe Pass type sound, you need a big empty box with an arched top.
Not really apropos, as I think this is still our of your price range, but I just want to give a strong endorsement for Heritage guitars. They are making the arch top guitars Gibson should (and used to) be making, in the old Gibson factory, with the old Gibson employees. Gibson has the name, Heritage has the guitars. My Heritage Golden Eagle is the only factory built guitar I have ever owned that I wish I had not sold. The Ibanez and the Cort (cheap guitars so that I didn't have to bring my nice ones to classes where they could be damaged by some twits pointy headstock) were crap, and I couldn't care less about them, but I miss that Heritage. It was a great guitar.
Actually, I hope it still is a great guitar for someone who will play it a lot more than I ever did.
Light
"Cowards can never be moral."
M.K. Gandhi