I've been using Kingsley pedals live for years and haven't had any problems. I don't have a Minstrel so I can't help with exact settings but I try to eq my dirty tone as close to my clean tone as possible.
I don't think you have to go crazy finding the right Tele for Page tones mainly because they are very varied throughout his career. Amp choices are important and a Tone Bender MKII for fuzz tones are more important than specific pickups and fretboard materials.
Please don't shoot me for what I'm about to say. Thick and rich are two adjectives that don't come to mind when I think of a Strat. That said, Strat players tend to thicken their tones by using pedals with extra mids like a Klon or Tubescreamer. My vote is to build a typical Strat and beef it up...
If 2x10 is what you're after then a Tweed Super sounds like a no brainer to me. Victoria is a good place to start. I have a Metroamp 50 watt and a Tweed Pro and whatever pedal sounds great in one sounds just as great in the other. A little dirtier in the Tweed however.
Page used a Tone Bender MKII with a Tele and various amps while he was in The Yardbirds. The MKII iz only used on 3 songs on LZI with a Tele and Supro. If you're after other Page tones it's best to look elsewhere.