The thing about the burger, though, is that it kind of IS, at the very least, the first thing that gets through to her, though.
She eats the burger, then the bithday train montage starts where we see her slowly opening up emotionally, then Bedman kills her dog.
I think It's also important to note, however, that bedman had only intended to kill the dog temporarily. And i don't mean in the sense that he makes another one. He mentions that he makes a point to remember everyone he kills so that when he finally creates his absolute world, he'd be able to bring everyone back as though they never died in the first place. Ramlethal's reaction to the mage hound dying and her realization that she's unique was Bedman's first hint that the Universal Will hadn't been entirely honest with him, which is why he gets so angry afterwards and immediately goes to confront her about that.
This directly leads into the tragedy of when he's defeated by Venom and Robo-Ky, because he had already been suspicious of UW by that point and (iirc) was about to start actively working against her right before that fight started.
So while we're still clearing up misconceptions, i'd like to point out that Bedman did not die because he was woken up.
He died because he deleted himself from the universe as the cost to create a small absolute world. UW showed up to gloat after Bedman had been defeated and explained to him that he absolute world plan was a lie from the start. Bedman gets angry and tells her that he was able to MAKE an absolute world, just not on the scale that UW had promised. UW was shocked because she didn't believe 1.) The absolute world was possible AT ALL, and 2.) Because the absolute world would theoretically be able to delete the Universal Will from existence. So Bedman creating an absolute world posed a significant threat to UW. But Bedman's goal from the start was to cure his sister Delilah. Even in revenge for being made unwillingly to commit mass murder, Bedman couldn't bring himself to ACTUALLY kill the UW.
Near-ish to the beginning of Sign, Bedman warns UW that he'd always intended to create his absolute world even before they'd met. The UW simply had offered a better option, and if that relationship would ever change, Bedman was always going to be able to just go off accomplish his goals on his own. UW writes him off because she doesn't believe him.
In one of Happy Chaos' arcade routes, he explains exactly what Bedman did as a way of explaining that Nagoriyuki can be used as a way of navigating across dimensions.
-the burger was significant because it was Ram's first positive experience,
-Bedman wasn't just killing her dog because he's evil, Bedman killing Ram's dog ALSO woke Bedman up to justice (neither pun intended),
-Bedman waking up wasn't what killed him, it was what allowed him to be able to kill himself (or possibly it forced his hand so that that was his only option)