I think you're referring to "Headphone output" rather than "Phono output". In which case definitely try the output on the Marantz with your Grado headphones. Grado are known to be very easy to drive and the Marantz will at least have more current than MP3 players for example. I do find that amplifiers and AV receivers usually have a lot more current/headroom though. If you have one with headphone output try comparing that to the CDP.
Then, in your own time, you can demo various headphone amplifiers to see which makes the biggest difference. Headphones are great in that they're very easy to take into a store/dealer and demo with various amps, and of course room acoustics is not an issue either.
Also, there's various DAC/Amp combos out there (Beresford Caiman, Firstone Audio, etc.) that will give you greater flexibility and are worth looking into. Some have a money-back guarantee so you can try before you buy.