Every time it looks like one guy, say Iga, has the inside track (gradually teaching Kae to be comfortable touching a guy with innocent handshakes), conditions allow for a shake-up. Enter Nana, who is concerned about being the least close to Kae of all the others.
When Kae, dirt broke from the pilgrimage, gets a job at a theme park dancing in a Puri Puri Moon show, it’s Nana’s time to shine, as he’s watched, danced, and sung every song in PPM’s repertoire every weekend with his adorable little sister Kirari.
As such, Nana is the one and only one who can get closer to Kae this way. The others try, but the hiring staff of Usami Land find other part-time jobs that better fit their particular skills and circumstances. As for Nana, he puts everything he has into training for the role of the Dark Prince, even at the cost of his health, suddenly collapsing with fever.
Kae has him brought home, then takes care of him by cooking him food before he takes his medicine. She manages to bond with Kirari a little, but not to the point Kirari is willing to let Kae have her brother, whom she wants to marry. But their shared knowledge of PPM is a definite ice-breaker.
Then things get dark, and I mean really dark, as a fever-addled Nana, essentially dreaming while awake, grabs, kisses, and holds down Kae, who isn’t strong enough to break away. If it wasn’t for an improbable Iga to the rescue, who knows what might have happened.
The show does not contend for a second that Nana was just getting the better of his hormones to awful result; he was well and truly not in his right mind. I have no reason to doubt that, and neither does Kae, but that doesn’t change the fact it was an awful and terrifying experience; one that makes her nervous about touching any guy again, including Iga, the guy she was making such nice gradual progress with.
After apologizing profusely both on the phone and in a very public display of begging outside Kae’s bedroom window (much to the chagrin of her older brother), Nana regains Kae’s trust in the heat of a PPM show gone awry, when three otaku n’er-do-wells must be dealt with, requiring Kae to take Nana’s arm/hand on numerous occasions.
I’ll admit the frozen faces of the character outfits were a little unsettling (not to mention an obvious trick to save money on animation), but that’s often how such theme parks operate; the labor they have at their disposal isn’t always going to remotely resemble specific anime characters.
Indeed, the frozen faces served at least two laudable purposes: they provided a literal “padding” between Kae and Nana to facilitate healing between them, and it also served as a semi-biting commentary on the culture of such shows: play the right tune and bust the right moves, and facial expressions, to say nothing of plot and character, are all irrelevant.