Your mention of "cuts through" makes me think you play in a rock/pop band, and that on some songs you need your AP sound to be heard along with many other sounds, but without stepping on top of them.
There are some piano sounds from Roland that really suck when you listen to them by themselves at home, but work perfectly for certain repetitive parts in a covers band. Try PCM 1 (128VoicePno). I suggest you put it in a studio set so you can reduce its sustain. Don't listen to it at home any longer than required, to get its default sustain reduced properly in your studio set. Don't play it again until you are at rehearsal with your full band. Then use it on some song like "China Grove", "Johnny B Goode", or any song that has a similar repetitive chucka-chucka part in its chorus. Don't make your final judgement on this AP sound until you have completed this test with your full band. Note that there are songs where this AP sound won't work - when we started rehearsing "Carry On My Wayward Son", the suckiness of this AP sound became quickly apparent during the rehearsal, and I switched to one of the other AP sounds in the Roland. (I have an FA-07, which has the same Supernatural and PCM sounds available in it as the Integra-7). Any song where the AP sounds are more prominent, or played with little else going on, will need something other than 128VoicePno.
I also have tried the SRX-11 in my old Roland XV-5050, but I never switched over to using its AP sounds in gigs. Because my FA-07 only allows me to download and use 2 PCM expansion cards at once, I don't even have it loaded in my FA-07. The EXP-02 is the real keeper - I cannot live without it - it contains the sounds from the old SRX-07 expansion card. I don't use its AP sounds, but use many other sounds on it. I also like some of the EP sounds in the EXP-05 (which contains the sounds from the old SRX-12 expansion card).
I have a Nord Electro 3, so I have experience with trying to find Nord AP sounds that work in a covers band, which is an interesting challenge if you run in mono. My Electro's organ sounds and EP sounds have caused me to use my Electro for those, and to not use my Roland for these except for one song where I want a very thin organ sound. Even when comparing to the EP sounds in my Roland FA-07 from the EXP-05, I find the EP sounds in my Electro 3 are much better.