I'm not a jazz fan, and I, too, found the jazz inflections in HEAVEN evocative and fresh. The show's best known song (if it has one) is a beauty, "The Only One," perfectly placed at the end of the first act. And a key phrase in it is reprised by O'Hara's Kathy in her second act meltdown, "Tuesdays, Thursdays," which is a harrowing, character-specific catharsis (I thought of it recently listening to "Days and Days" from FUN HOME, with which it shares sentiments about being tethered to a demanding absent husband. Worth noting: both are songs by wives of closeted gay men.) But I also love "Sun and Shade" and the exquisite "Miro."
The PH production was undermined by a truly awful design plan, a kind of metal skeleton onto which pieces were clumsily added, against projections that maybe too easily evoked (and reminded us of the origins via:) the stunning cinematography in the film. I'd love to see the show done not necessarily in a physically pared down way, but in a bigger, emptier space. No one had any breathing room at PH, and despite wonderful costumes, the period didn't seem authenticated. I wonder if Pasquale's "I Never Knew" ever makes it into cabaret spaces. It's a tough, start-stop song, filled with introspection (again, a little like Bruce's "Edges of the World" in FUN HOME, but without the final despair). Pasquale's performance of it is a wonder, and the NY Times included it in its on-line performances.
"I'm a comedian, but in my spare time, things bother me." Garry Shandling