I have a stock SH-12 in the neck with my Dimebucker in my Walnut San Dimas and I don't have any output/volume/more gain required issues between those...I also switch back and forth between my Walnut and my Basswood that has the SD in the bridge so the output difference between the Dimebucker and Screamin Demon thru my setup.
I guess from my perspective–I tend to go with higher output pickups (JBs, Dimebuckers, Hotrails, etc.) but I found that the Screamin Demon acts like a higher output pickup but handles/responds to the volume knob better than any pickup I've used.
Lets go full circle here...you like the sound of the SH-12 from videos and clips–but you've never played one--correct?
There is more than one way to get a "good rock rhythm and lead sound in the bridge"...like so many options here. From Seymour Duncan's description it can handle that:
Application: Moderate output, P.A.F.-style with added "growl." Great for classic rock, jazz-rock fusion, heavy rock and aggressive instrumental rock.
Description: This pickup was designed in the Custom Shop to provide the big open sound of our '59 Model with a little less bite and a little more growl. The tone is big, percussive with a defined treble response that doesn't get harsh. It uses one row of allen screws and one row of standard slotted screws for a unique "airy" sound. Comes with four-conductor hookup cable.
I personally love the way the SH-12 responds–very unique pickup that gets super sweet with the guitar's volume knob turned down but then can growl and yell like crazy with it cranked and the gain added on. It wails during hard hitting songs when I want it to and then tones down to soft and sweet when I want during the softer songs...one of my favorite pickups.