GeneralRevision Ideas:

About Anna's active ability. There is only one exposure currently, and I was probably trying to translate her AH ability a little bit too faithfully. Instead, I think I have a solution based around the particular nature of her Personal Story in AH. To do so, I will have to alter her stats around.
Lore: 2 Inf: 1 Obs: 3 St: 3 Will: 4
Action: Spend one Sanity to test Will instead of Lore when resolving spell effect that may be used during the action phase.
Passive: Recover 1 Sanity when Anna passes a Horror test.

In regard to Astrid's once per game ability making her a use and sacrifice type of character, you are correct. I want to avoid this, but still give her a powerful rumor-based ability.
Astrid's action will remain the same, however her passive will read either (1) Passive: When a rumor is in play, Astrid receives two additional dice to all skill tests. (2) Passive: Gain up to two improvements for a stat of your choice when a rumor is solved. Thoughts?

With Anton, I would like to keep his passive slightly better than Voice of Ra (otherwise I would have given him the spell to begin with, but it does raise a question about power creep should he end up with the spell as well). I'd also like to permit his action to happen after the encounter phase to keep him interesting, but also to allow opportunities like closing a gate, but then being able to begin the trek to his next destination. This third action could not be a duplicate as per the standard rules. I might change this passive, but only if it becomes a mechanical problem during playtests.

Hosea's action ability is really quite powerful and unique allies do not come up very often. There has to be a significant sacrifice to obtain them as he can trade his allies away since they are assets. I'm more worried, actually, about how powerful he may be able to make the team if someone uses Feed the Mind on him continuously. Tasks are QUITE good themselves, but they require specific goals to be met to activate them. Doling them out to those most suited to the task would be costly in terms of actions. I think the Doom track keeps him from making the team too powerful in a typical game, but I should probably playtest this first. Also, the lantern is a relatively insignificant item, but it is thematic and I think a one-time use. I will check when I am home.

And finally, one possible thought about Obi's active ability which may be too confusing for simple play. Action: Return an artifact you own to the box and place a "!" token at your location. If a gate would open there, retreat the doom by 1 instead and remove the "!" token. Artifacts are pretty rare, and quite a trade-off for doom reduction, but it is a powerful ability. Thematically this item discarding idea relates to his ability to create Gris-Gris (a type of beneficial spiritual totem) from items of significance or power. If you want the whole story, check out the Arkham version's "the story so far/personal story." Also, his passive does effect all investigators board wide. This is one reason why he is a 8/4 character. They are significantly harder to keep alive, and most 8/4 characters have this trade-off. Jacqeline's clue trades & gains, Charlie's asset buying and action transfer, Georges's ability to free detained/debted investigators board-wide, etc. There are exceptions, but I believe this is one of the balancing ideas that has been in place since launch.

Edmund is a little difficult to feel out. This is mostly because FFG has not shown us how or if Wendy is going to compare to other investigators. In Arkham, Wendy started with one of the most powerful items in the game but had significantly lowered stats. The Silver Key in Eldritch is pretty good (it is also a part of Edmund's original back story from his AH version). I'd like to keep it, but, again, I'm worried about people just trading it and then letting him die. I could add a "The Silver Key cannot be traded" addendum, but it has yet to be done in EH, so I'm not sure if I ought to implement it. Thoughts?

Are these improved ideas? Or do these only complicate matters with these characters? Thoughts?

I'm worried about people just trading it and then letting him die. I could add a "The Silver Key cannot be traded" addendum, but it has yet to be done in EH, so I'm not sure if I ought to implement it.

Even with such clause, players may still kill him and loot the body. Unless you also patch that.

You may also decide that you don't care about the potential abuse. If some people consider dying on purpose a fun way to play the game, you don't necessarily need to deprive them of this possibility.

It's possible for Edmund I could always create a "In case of...." encounter that discards either all of his posessions or just the Silver Key. Actually, having it mysteriously disappear could fit right in with his story.

I think there are at least a couple of new investigators that specifically tell you not to take their posessions, and, instead, if you pass the test you get an Artifact or something similar. So it's not unheard of for these post-death encounters to take an unexpected turn.

This incorporated with a "Edmund cannot trade the Silver Key" adendum could solve the problem. I feel that he should still be able to lose it.

Thanks for the thoughts. All the feedback I've received so far is really helping me along with the next iterations, which will likely be play-tested before finalized.