The Fat 50s on my Strat are way hotter then the HB on my Soloist.
Really? What's that HB in your soloist?
If that is true then indeed all the rigs would sound over saturated with your Strat, but I'm surprised because I'd have considered the fat 50’s as overwound, but still vintage, pickups.
Personally I prefer slightly overwound pickups for my Strats myself (Fender Tex Mex's and Leosounds Red House (from Germany).
Still my Tokai Les Paul (PAF equipped) saturates my rigs more than the Strats.
And I like that because that's how it is in real life as well.