Hi James,
believe it or not I've ran some really good marketing campaigns in my time.
There are two ways to find a good slogan for your company that I know of.
A. The first way is through identifying the qualities of your brand.
B. The second way is by listening to what your target audience likes to call you or say about you.
Then the question is what you want to do with this information. Do you want to build a household brand? Do you want to build a connection with prospective customers? Do you want to build market awareness?
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Let's look at A first. You want to figure out why people are buying your brand. Then, you talk to them and try to solicit personal stories that have to do with these qualities. For example, if I understand your brand's placement in the market correctly, the following qualities of Bryston matter to people:
1. Bryston is a standard of quality. You will find it in many places where quality is paramount - recording, mixing, and mastering studios. Working musicians who don't want outages. Mastering engineers who want the most appropriate reproduction. It's not flashy, it won't make your head spin - it's quality like an old nut cracker.
2. Bryston is so good, there isn't really a reason to go up any more. The amazing distortion, noise, and headroom figures mean that you can take a Bryston amp and it will be extremely competent in any situation. You buy Bryston and then you don't have to upgrade any more - you're done. You can, there's always some way to slightly upgrade here and there, but you don't really have a good reason to.
3. Bryston is made to work for 20 years. It's made to never break, and if it does, then that's rare.
4. Bryston repairs are very generous. The company cares about its customers, and you clearly cultivate a great and personal relationship with them.
You'd also want to ascertain if there are any others people are interested in. Once you're done gathering this sort of information, you'd take these qualities, and just start talking about them. Have people describe them in their own words, and how they relate to their use of Bryston equipment. Listen to them carefully - during phone calls and the like - and write things down in transcripts. Review the transcripts periodically. Somewhere in there, one phrase will show up that will resonate with you quite well. For example, in what I wrote above, "A Standard of Quality" is one such phrase. I think this describes Bryston really well and makes it patently obvious what you guys are aiming to do with the brand.
Let's talk about B. To recap, it's: "listening to what your target audience likes to call you or say about you". Often, brands will get nicknames, or people will make memes about them. One time I heard about a guy who bought a crappy beaten down Bryston on eBay that was completely broken for $500, sent it off to you guys, and got it back in perfect condition for pretty much free. I don't know if people have nicknames for Bryston the company. Or maybe the users have pet names for /their/ specific Brystons. The closest I came to that is "those crazy Canadians who use those annoying square screws from Canada and getting a bit for those takes two weeks". But I don't know that people will immediately recognize you for using Robertson screws. (yeah, P. L. Robertson was Canadian). Talk to your audience, see if they have a favourite nickname for their unit. Something cool might come out of that.
I think you did great by coming to the community and asking about slogans and the like. Consider doing the "personal stories" thing, and give it a good effort. Maybe if you hear some really good testimonials, you could even get people in front of a camera, in a really cozy lighting scenario, just have them recount their personal journey towards, and then with, Bryston. I don't think you'll find a more passionate people than high-end Hi Fi enthusiasts, and if someone has something from Bryston, they didn't just walk into a big box store and buy it together with a blender, a microwave oven, and a pallet of energy drinks. They had to arrive at that destination. Maybe it was an epiphany at some point. Maybe it was inherited. Or, like with me, random encounters, spaced out over decades, that led to almost 10 years of hunting for an affordable set. If you can capture this enthusiasm, then it will easily inspire other people who love the same subject. Maybe they'll go and buy Kef KRK instead, but you'll be the ones inspiring them, and that's worth much more than any immediate purchase.
More than anything, I'm sure you'll love to hear about how your users relate to Bryston. That'll probably be a really good reason in itself to do this sort of research.
