From my ownership of Mules, Manhatans, S.Ms and M.Qs , ( and for your balance of usage ) M.Qs would get my vote.
M.Qs will give you a tighter / punchier bass end and assertive yet smooth high end detail for double stops / 50's Rn'R riffs. ( on the M.Qs , Pickup height adjustments can modify the top end between glassyand fat, to sweet yet biting ).
The AII Stormy Mondays are lovely pickups, if you had stipulated 80% Jazz / 20% R'n'R .
Manhattans are ( for me ) 100% Jazz .
Mules would also be favourites, but there is something about that M.Q sound - that breathes life / a unique tone into a semi-acoustic. :)
The last point to consider is that M.Qs are a low noise / hum ( i.e. encased in a nickel 'cage' ) single coil, and the Mules hum proof. Whilst I have never heard single coil noise on my own M.Qs, I feel it only proper to at least mention that it is theoretically more probable than with Mules. :)