A basic approach would be to estimate the air-pressure at the top of the mantle.
Uranus' surface gravity is a bit less than Earths, but, somewhat counter-intuitively, it's atmosphere is light enough that it's gravity increases as you move inside the planet towards the top of the mantle. (the same is true for Earth). For ballpark estimate, lets say the gravity works out to be about the same as Earths, because I don't want to calculate, but it might be a bit more than that.
The Mass of Uranus' atmosphere, by Wikipedia is about 0.5 times the mass of Earth. It's surface area is about 16 times Earth (4 times the Radius), but the surface area of the Mantle would be less, about 80% of the radius which works out about 10.2 times the surface area.
If you spread 0.5 Earth masses over 10.2 times Earth's surface area, you get a pressure between 50,000 and 60,000 atm. Some 50 times the upper limit you provided in your question. That's probably a limiting factor for most "ice giants". There's simply too much hydrogen and helium atmosphere to allow liquid water at 1,100 ATM. Ice giants might create their own hydrogen by heat and pressure on Methane, creating diamond like structures and free hydrogen.
The heat below all that atmosphere (about 20% of Uranus' radius) would be outside your criteria too. I couldn't find any good estimates for Uranus' mantle's temperature. There's too many unknowns about why Uranus is as cold as it is on it's surface, so estimates on it's mantle temperature seem pretty tentative and unavailable, but what little I know about how temperature rises inside a planet, I don't see any way the top of Uranus' mantle would come close to the temperature criteria you gave. Not at a depth of 20% of Uranus' radius.
Consider this chart from Uranus' wikipedia at 200,000 mbar Uranus temperature is approaching 340 K. 200,000 mbar is about 200 atm. The mantle begins, by my ballpark estimate at about 50,000 atm. The temperature wouldn't be close unless the planet had a very long time to cool down, perhaps tens of billions of years.
I could run ballpark estimates on Neptune too, but I suspect the results would be similar.
For an ice giant to meet your criteria, it would need to have comparatively very little hydrogen and helium compared to Uranus. Perhaps if an ice giant was close enough to it's star that it had a hot enough surface temperature to lose much of it's hydrogen and helium through Jeans escape, and then, it had a long time to cool down, it might get the right criteria of liquid water at the proper range of temperature and pressure. I don't see any other scenario where it would work.