When I first got into guitar, it was the Dual Rec era, and then in college I got heavy into SRV, so two totally contrasting sounds there. I still appreciate those sounds, but started to explore other things in about 2010 when my band situation changed, and then since C19 happened and my playing situation changed considerably again, my desired tones have as well. I'm enjoying the cleaner into medium gain tones these days, although I still call up high gain tones on occasion.
But, if I had to distill something consistent about the tone that I want, it would be that there has to be the right presence to the sound and treble articulation, contrasted by appropriate midrange. Much of it ends up coming down to speakers, the amp plays a part too but if the speaker is wrong, there's no fixing it. I need to have enough sparkle to sit well in a track and not sound like the "blanket over the amp" or "far away" guitar tone, treble to bring out single notes clearly, but also needs to have girth to the midrange that keeps the sound from being brittle. It's a fine line. I have high hopes for the HDRX 20 being a good amp for the things I like.
I know you already grabbed some pedals... but I'm not going to pretend any of us are ever done buying pedals! The BE-OD is a good rhythm pedal, maybe leans more modern than 80's tones, but IMO where it's really at with the Friedman pedals is the Dirty Shirley. The BE-OD has a less prominent midrange, and not adjustable, maybe not fully scooped but definitely thick and not particularly cutting, and just a TON of gain. The Dirty Shirley hits the spot, especially when it comes to great 80's sounds and lead tones for any era. Still has plenty of gain. The Smallbox is a good one too, but definitely sounds like a Plexi no matter what, whereas the DS just kind of melts into your rig, in a good way.
I think the DS got lost in the mix after the BE-OD was the flavor of the week for a while, and then the DS came out just as the commotion of the BE-OD started to die down.
If Friedman released a dual pedal with the BE-OD on one side and the DS on the other... mercy.
I'd really like to try a Stiletto sometime. I stupidly passed one by about 10 years ago because the guy at the shop told me I wouldn't like it, but the lead sound Andy Timmons got out of the Stilettos when he used them was tops. I'm not saying his tone now is bad, but it hasn't ever been as good as that.