just an afterthought / clarification about my vote for 'Cold Sweats' in your particular guitar :
Whilst my Les Paul ( for which I would have envisaged C.S. to be very flexible in ) - is mahogany with the usual maple cap ; I do have a nice 335 type copy - which is basswood ply / mahogany neck - and in that , the bass needed a little help to stay tight enough for my ( still vintage ) tastes. Again, I am no expert on tone woods, but my Strat ( basswood body / maple neck ) used to be fairly neutral tonally, so I assume the Basswood characteristic I heard in both, was a somewhat softening influence.
So, whilst I presume that 'Mules' might be lovely in your guitar for purely classic 60s - 70s Rock / Blues - the C.S. seems to offer an expansion on that basic tone, but the added assurance of a tighter, more 'biddable' presentaion.
The reason I respectfully assume that C.S may be then more apt for you than ( for example ) Rebel Yells , is that we want to keep one foot in the 70s - and a foot in the here and now, tone wise. I'm thinking neck pickup for Gary Moore/ 70s influences - and the bridge for all else 80s and beyond.
I hope you find something you like . :)