I think that is statistically impossible you definitely need the heart scrolls from the lovers in order to clear the board. Sorry I'm going to stay skeptical until further explanation
Unfortunately I don’t have proof but it took me a very very many runs to get it because you need to get lucky a lot for chests and scrolls.
Also, I think you misunderstood my comment. I definitely used the lovers to clear the board but only after I killed the dragon and got the first three achievements.
I will say I spent over an hour on that one run because, especially at the end when I didn’t have a lot of hearts, I would patiently do test cases. Basically, I’d use the book and come up with all the combinations of leftover creatures within a given area (say a 2 by 2) to see which would contradict the board. That helped me progress quite a few times. And I was lucky enough to have enough coins to reset after killing the dragon, so clearing the board was trivial after that bcs I still had R&J.