+1 on the look of that guitar.
I'm going to suggest Mules or Riff Raffs, leaning slightly towards the latter.
I use mine for roughly the same sort of music as you do.
My Riff Raffs are in a mahogany body/neck, rosewood board, Gibson Explorer. My Mules are in a Japanese Tokai Love Rock, same woods as yours. One day I'm going to try swapping them over just to see what happens.
I personally struggled with the Mules to start with - I think I was expecting something "different" from what they actually do (I'd already been using the Riff Raffs for a bit, and was lusting after the "vintage late 50s sound"). However, I have grown to love them (after buying the Love Rock to house them!)
In my experience, the Mules seem to have "more" of everything (top and bottom end) but with a more open sound, whereas the Riff Raffs seem tighter or more "focussed". I think I had to learn to appreciate the openess of the Mules. But anyway, my experience might be the guitars they're in - which is why I'd like to swap them over one day, just to see...
I don't think you'd go far wrong with either set - what you really need is another guitar so you can have both!
EDIT: Sorry just reread the end of Twinfan's response - I've not tried the SMs, but from all I hear, and if you need the "cleaner" end, SMs might be what you're after. The Mules, with my settings, clean up into Paul Kossoff territory rather than Dave Gilmour. I don't know how to describe the clean of the Riff Raffs in my Explorer - I'm using it pretty much like Allen Collins in Lynyrd Skynyrd most of the time, or as my stock blues-beast, or as a "Ricky Medlocke in Blackfoot" sort of weapon!