Phase noise is going to be a product of your OCXO, not really dependent on long term drift, so while a GPSDO can often make a decent source, it's not inherently any better.
Your current reference isn't too bad in the phase noise department, does it not output a sine wave? You could look into a GPSDO with a better OCXO used for the absolute reference, or even a rubidium or disciplined rubidium source, but again those aren't really going to have a bearing on the phase noise inherently - it just depends what their output oscillator is derived from. Some rubidium sources are derived directly from that physics package, so they are pretty bad for phase noise, in the case of the PRS-10 (which I agree is great but have had no trouble with disciplining), the rubidium disciplines a high quality OCXO internally, so the basic 10MHz output is very low phase noise since it's actually an OCXO disciplined by the rubidium oscillator.
This also means that if you need low phase noise only, a high quality free running OCXO should do just fine, and any piece of gear with a good OCXO reference with an output may suffice for that.
But what do you actually need a 10MHz phase noise reference for? As phase noise is going to be a product of the PLL or disciplining loop of what you're working with, having the lowest phase noise 10MHz reference isn't actually a huge deal - unless its egregious the equipment referenced to that dirtier 10MHz signal should be able to do better if they are designed for it. Generally you are concerned with phase noise with your LO or RF tones at whatever frequency they're required at, so unless you're going to be transmitting at 10MHz directly, it's not that critical that your 10MHz reference is super clean in terms of phase noise. If you want a reference beyond 10MHz (or even below), I'd look at either a fixed output one like the Signal Hound PNCS-1, or a very low phase noise generator like a PSG generator or a Holzworth generator, or something comparable. As mentioned before, these low phase noise generators don't even require an external 10MHz reference to achieve their output phase noise performance because it's a factor that depends on the internal PLL design and architecture.