For a "HUGE" improvement, I think you need to move up to the next level of CDPs. These are typically CD/SACD players or CD ONLY and don't include DVD playback.
The higher up the chain, CDPs will (sometimes) have a better DAC, and most certainly a better master clock to prevent jitter. Lack of jitter control is what causes that "glare" or harshness from a CD.
For example, the Musical Fidelity M6CD would fall into this category, and the higher end Marantz. If I was to put a price on this level of CD, it would be $2000+. Of course there are some exceptions.
The higher up the chain, CDPs will (sometimes) have a better DAC, and most certainly a better master clock to prevent jitter. Lack of jitter control is what causes that "glare" or harshness from a CD.
For example, the Musical Fidelity M6CD would fall into this category, and the higher end Marantz. If I was to put a price on this level of CD, it would be $2000+. Of course there are some exceptions.