Well, as an 'oldie' who plays low gain pickups through valve amps, I only have two points to mention- although nothing conclusive .
1) There are some great sounding solid state amps out there. The sound being 'different' but not inferior.I.M.O. Iam thinking of some Fender amps I have played through, and one that I own. Warm but tight. I am thinking of the great sounds acieved in the 70s by the Telecaster wielding Wilco Johnson of 'Dr. Feelgood', ( a humble H & H brand solid state amp ). Then there's B.B King's love of the 'Lab series amps that where part or whole solid state - and a Yamaha head used by Doyle Bramhall II during his playing on the the Roger Waters ' In The Flesh' tour / DVD.
2) I read somewhere that a current 'Metal' player ( who's name escapes me ) likes the ultra quick response he gets from a solid state power stage. I gather from this that a reallly tight, high gain B.K.P would sound deadly through your Randall. Your existing 'Miracle Man' bridge pickup should be a taste of things to come !
I agree that B.K.P. shine through many types of amp though.I am currently jamming /playing through a Fender (solid state ) G-Dec Junior, and each of my B.K.P sound as recognisable through that - as through my all valve gear.
I prefer certain qualities of valve amps though, for what I play - and the way they replicate the sounds I am most drawn by. I have ( and would ) gig through a solid state amp though. If you can get what is close enough to your sound out of a rig, then it is doing it's job just fine. :)