The Mule is an excellent all-rounder - don't be put off by its output, it can handle any everything up to and including the most extreme metal styles. The output level means the dynamic range is superb, and the pickup has a very open and clear voicing.
However, if you want something with a fatter and more focussed sound, the Black Dog is based on the same "recipe", but is overwound to give a very meaty sound that is still dynamic and punchy.
Either would be excellent for the styles you've mentioned.
The Mother's Milks are much cleaner sounding than either the Slow Hands or Irish Tours. They have that woody 60s-style strat sound that guys like Frusciante are well known for, with plenty of "cluck". They would match up very nicely with the Mule, and the Black Dog wouldn't overpower them either.
The Slow Hands have considerably more midrange, giving a fat and weighty tone though still retains the traditional stratty top end.
The Irish Tours are closer to the Mother's Milks in voicing, but have more low end push and a naturally gritty sound as though the guitar has huge strings on and is being attacked a la SRV or Rory Gallagher. I wouldn't describe them as thin sounding, though they might not be the first choice for a particularly bright strat.
So, overall I'd recommend the Mule or Black Dog with Mother's Milks. However, if output is a worry (and I truly don't believe it would be, but you may feel uncomfortable risking it), a good choice would be a Nailbomb bridge with the Irish Tours. The Nailbomb may be from the contemporary range, but it's remarkably open and dynamic for a pickup of that output, and has an rich, old school voicing that would suit the styles you've mentioned.
