Hades 2: Are some gods more or less common?

I'm trying real hard to collect all of the legendary boons, and I'm not sure what counts as a spoiler so I'm going to go overzealous.

My problems right now are Haphestus and >!Hera!<where I can't even expect in a run to see them enough times to qualify for their legendary boons and get them even if there was no random chance involved. I'm using >!every arcana that helps selection!<and obviously the respective trinkets but I'm routinely seeing my chosen boon provider 3 or fewer times in a full run.

I've been spending more time on these last 2 than I have for every single other God combined, >!except Chaos who is pure RNG but it happened so that's fine!<and still on a good run I see my chosen God 5 total times. I've had little to no luck >!rerolling the doors themselves!<so I have to assume that's not part of the intended strategy.

I wish more legendary boons were like >!Hermes!<in terms of requirements. >!Can you even get Haphestus's legendary boon if your weapon is max rank?!<

Is there a way to manipulate things to see a chosen greater god more often? >!I've learned that having 3 gods amongths your attack ,special, and cast mean you will always see trial of the gods with the 2 you don't care about!<though that may be just my bad luck. >!With Hera specifically I'm trying to avoid Zeus entirely because I don't want their duo boon populating the already crowded list.!<

Any tips help.