A transport could help. I don't think it will reduce the treble of CDs per se - you shouldn't be losing that information anyway - but it can make the highs sound smoother while solidifying the foundation of the music (mid-bass down) which will balance the sound. Usually high jitter/bad transports sound very thin and weak which makes any recording brightness harder to take. Think of it more in terms of overall balance rather than one particular thing.
Your poor experience with Blu-Ray transports does not surprise me. The clock circuits in video players is a lot messier compared to a dedicated Redbook player/transport that only needs a fixed clock for 44.1k.
I don't have a ton of experience with transports but the best I have used was a now-discontinued April Music Stello top-loading CD player. With a Monarchy NM24 DAC, it was miles better than a mid-priced audiophile CD player (maybe Atoll) that my friend had. But my Onkyo DX-7555 CD player, which has a "high precision clock," was a close second and made a very musical transport that I was happy with. Unfortunately I tossed it because it was too big to fit in my cabinet, and replaced it with the cheaper C-7030 (~$150) which isn't nearly as good. I'd be willing to bet their C-7070 (~$700) is a pretty good transport for the money, but in that price range the Cambridge CXC is probably a better bet - it's on my list to try.
Another thing to try is a PLL/signal conditioner like the Monarchy Audio DIP. Get the Classic one, without oversampling. It greatly reduces the gap between a mediocre and good transport and can add a lot of body to the sound. And yes, SPDIF cables do make a difference, as much as I hate to admit.