I don't have a quick fix for you. Actually, I have a question about the brightness you hear. Is it bright compared to other similar budget systems you've heard?
Here's why I ask. While you have a nice first system, almost any system in a similar budget range will have a degree of weaknesses. Brightness is often the problem because the components (especially speakers) will not be totally neutral and full-range. In addition, solid state components at a budget level will usually have a degree of glare and artifacts that can be associated with brightness. Budget CDPs are particularly bad in this area especially when attempting to listen at higher volumes.
What's the solution? Unfortunately, there probably is none at $150. My advice would be...
1. Don't stress over it. The curse of this hobby is that everytime you reach a certain performance plateau, you then want the next level. Trust me, you will probably one day have a system 2-3 times as expensive as your current system and still find things you want to improve. Ironically, it's that goal and potential for achieving something more that makes the hobby fun.
2. With $150, there ARE a few tangible things you can do to improve your sound. Unlike other suggestions, I would NOT start exchanging cables. Your cables do seem to favor the speed and clarity side versus warmth and liquidity, but they are plenty good enough for your current system. I wouldn't waste time and money on lateral $150 cable moves.
Instead, I would look at various tweaks for $150 that could improve your system more than you might think. In particular, room treatment and isolation devices would be where I would focus your attention. Almost any budget CDP responds well to isolation devices and they are relatively inexpensive or can be DIY. Same is true for room treament.
Despite having over $6000 retail in amps, $4500 in a preamp, $4000 in speakers, $2000 in CDP and $1000 in cabling, my system would still not reach its potential and keep me listening for hours if I didn't have a properly treated room and some of the inexensive but effective tweaks I use. Tweaks are also fun and teach you even more about how important EVERYTHING is to achieving the best possible sound.
Good luck