I saw this on Wednesday (just over a week before opening so probably close to being frozen?) and maybe it was because of all the negative reviews here, but I thought it was a lot better than I expected, a generally enjoyable if sometimes clunky show. I didn't know the book or movie so I thought the story overall with the way it integrated with the movement/circus acts was pretty cool, though admittedly somewhat trite (it's really not that far off from the extremely trite story that Paramour told).
I agree that the framing device is probably the biggest issue of the show. I thought the ending was sweet, but the way that older Jacob kept interrupting the show felt like it was just stopping all the momentum, and it seemed like the only thing that really gave us was to foreshadow the "Great Stampede". It also just felt like they weren't ready to commit fully to having Jacob retelling the story of his life--his narration all but disappears in the second act, outside of being in some of the musical numbers, so what was the point of having him there? (At least in Harmony it was done to create a picture of survivor's guilt). Some of the later musical numbers too seem like they're doing a song and dance number that's somewhat reminiscent of what's happening in the scene, but doesn't directly tie in (a bit like Cabaret/Chicago), and I thought that could've also been an interesting approach to take given the circus element, but it didn't happen enough to feel like consistent storytelling.
I thought the music was fine, and at the very least it was nice to hear a different kind of sound for a new Broadway score, but it seems like it doesn't quite crack the code of what a musical theater score should do, outside of a few specific songs. I think if they had taken the Cabaret Emcee approach with doing certain circus numbers that would be somewhat tied into the plot as an explicit decision this could've worked, but that never felt like their actual intention. I liked some of the montage songs like The Road Don't Make You Young and Zostan (though I have no idea what this song is supposed to mean), and Easy and Squeaky Wheel both worked for me in different ways, but the rest of the score felt mostly like it was talking around a point rather than addressing it head on (like a lot of pop songs tend to do). Though I feel like this could be a score I end up listening to, even if it doesn't necessarily work in the theater.
I haven't seen Pippin, and while I agree the circus stunts aren't as impressive as Paramour, I do think they're integrated really nicely into the show, whereas Paramour really just sketched out a thin plot for the purpose of showing off the stunts. I thought Easy and the other part with the horse was beautifully done, and while a little long and unclear as to its purpose, the fever dream in act 2 was pretty cool to watch in how it was stylized. The puppets were mostly fine, not as bad as I was expecting. The horses in general I thought were decent and the animals in The Lion Has Got No Teeth were adequate, but I'm not sure if the mixed mediums for the elephant worked for me with the way that they'd show different parts at a time. The puppet itself was okay, but just looked a little off (maybe the head needed to be bigger proportionally?), though I do wish they had gone a bit more of the interpretive route just so they could have the elephant do more things.
I definitely agree that Paul Alexander Nolan is the standout of this cast--he definitely has the most stage presence and made The Lion Has Got No Teeth a fun song to watch despite the lyrics being fairly elementary. The only thing is (and this is probably more on the direction/book) he seems to exude menace a little too early. Based on the Wikipedia summary of the book, it seems like it should be a bit of a surprise that August has a capacity for violence and cruelty, but there feels like there's always an evil glint in his eye right from the beginning. I liked Isabelle McCalla and she's great in the role, but nothing about the role really stands out (what even is her act anyway?), and Ken Wulf Clark was on for Jacob in my performance, and I thought he was quite good as well, but the material just didn't give him room to really develop a character.
I don't really expect any super positive reviews for this (probably mostly mixed to negative) but I did think it was an enjoyable watch, and if I knew people who like seeing circus elements, then I'd probably recommend it to them, though I wouldn't necessarily tell people to go out of their way to see this show.