I've been playing long enough that I've got several Lesser Hearts with various +X factors in storage.
That said, it is also worth noting that, with the exception of the Tiefling Scoundrel (which ironically is the only Iconic I've played), all of the iconic classes correspond to very common one or two level dips;
https://ddowiki.com/page/Splash
In short, you can easily take just one or two levels of the class required at first level and then build the character as another class (or classes) and not have to worry about the 'forced' class coming in to play in determining the past life feat.
That said, it is also worth noting that, with the exception of the Tiefling Scoundrel (which ironically is the only Iconic I've played), all of the iconic classes correspond to very common one or two level dips;
https://ddowiki.com/page/Splash
In short, you can easily take just one or two levels of the class required at first level and then build the character as another class (or classes) and not have to worry about the 'forced' class coming in to play in determining the past life feat.