Erik makes a great point. Don't worry about what you would have looked for in years past, look for something that is just enjoyable to you. I bet the speakers you would have had will be different from what you will want now. Personally, I wouldn't look at the EQ first, only because you MAY be able to find the right speaker first and if so, you won't need the EQ right away. Maybe in time you will, but strip it down to see if you can find anything that you love. If not, then you can start to match amplification, source and then EQ. I think I'd also just stick with one of the cables that are highly neutral and not try to 'tune' in that way. I'd go Erik's route at that point and go EQ. Cardas and Audioquest copper based cables will be easy to find and very neutral. Any dealer should be able to help you out in this situation and it's where they will be worth their money. You'll want to take everything home and set it up in YOUR room (one of the posters mentioned your own room tuning) and in this case, it's paramount. Some gear will just sound different at your place than in their's so you'd want to make sure that you love it in YOUR environment.
In regards to chasing a speaker, I'd personally start off with this in mind. Look for a speaker with pistonic tweeter and a clean waterfall plot and listen at lower levels. Alloy tweeters properly designed with an acoustic damper (in a few examples not just a finger guard) will always be lower in distortion and therefore less likely to bother one who has tinnitus.
There are plenty of companies who claim to be more pistonic than others, but sometimes just aren't. I'd also do searching to find out which companies tip their upper end a bit to make them sound more dynamic or exciting. I'd personally stay away from that as it's not doing to be right for you. Many of the top brands discussed on the boards have always done this. I don't think in the long run you will be happy with any of those.
What is your price point for new system? Again, I'd personally do even more listening than usual and do it as a full system and not as changing speakers. Nothing wrong with blowing things up and starting over if you are financially able to. If not, try to bring your gear into the store if needed to audition some speakers all in a day or two (if you are close you can go back to back days if needed).
There will most probably be a few speakers that will be pistonic in nature and enjoyable to you, especially if you have the help of a great dealer who knows what gear goes best together.
