Just half of the people who commented and many more.
I like how everyone has Heather as a given for E4 spot. I believe she was defeated (or just beaten) by Blake. An E4 or champion could fend for themselves and find a way to avoid capture. The reason I doubt this is the mere fact that if Heather is indeed E4, we will have to fight two dragon masters consecutively (hypothesis: she uses dragons). Given that Dragon is one of the most powerful types, and as such left for the last positions, Sapphira will be challenged right before the E4, or at best second last. Therefore it will feel monotonous or even bad to see us battle another Dragon tamer in the next episode. Given how limited our choices on dragons are, without the legendaries, we will be fighting two very similar teams. That is something nobody wants, and especially Ame, because we've seen that the gym leaders so far only seldom own common pokemon. Even if they do, some things get changed in their teams for it not to be noted.
Sigmund cannot be an E4, as he is too weak for the spot. This is actually the same reason Sirius is not considered a viable choice. They have been beaten and they had low-level pokemon. Remember when we battled alongside Amaria, an established gym leader? Her Lapras was lvl75 (now 80) which means that she already had a high position. If Sigmund owned another, wouldn't it make more sense for his pokemon to be of higher levels? I know that in that case we wouldn't beat him, so he could battle us in a fashion like Elias and Solaris.
Arkhidon Arclight could be a choice, since he hasn't appeared much, if only for brief moments trying to see what's going on with bombings and the pokemon black market. Him being an electric type trainer is more than obvious. However we already have 2 of those: 1 good and 1 evil. He's just... redundant. Unless he develops like Fern (who didn't stick to his grass pokemon) and gains a new role in the story, even as a dj in the nightclub, I cannot see him in the upper positions.
Solaris is a cool guy and really promising. He's not weak, and you were not supposed to beat him in Pyrous mountain (regardless if we did). Given T-Tar is on his side, a powerful sandstorm team is to be expected, and this is much fitting for a complete battler. I am willing to bet he has a position of power in the league, now that he no longer is occupied with leading Team Meteor (working more as an executive producer). Hence him having the position of the champion is possible.
Anna is a weird case in the essence that we know nothing of her. Fanfiction wants her and Noel to be Radomus's children. She is hinted to have a position of power so an E4 place seems quite fitting. It has been long since we fought the Psychic gym and her team cannot have a different type, as far as I am concerned. Therefore E4 is where I'd put her. She is assumed to be higher than Luna, who was once the Grass type E4, but I can hardly see her as a champion.
Elias is more or less established to be in a position of power. We already know he uses Normal types (Ditto and Snorlax are some), a type many people underestimate, but few dare to challenge. Be his position and E4 or an executive who replaced Ame is yet to be seen. Serra seemed to treat him like her guest, which means she is familiar with him. Be it that his eyesight miracle has been broadcasted by GG all over the region and he's a celebrity, or he has a E4 (which I believe to be the truth) is yet to be officially revealed.
Blake is another interesting fellow. He is not the gym leader, as the position is currently occupied by Serra, and I believe it has not been shown for him to be a leader that retired, much like his younger brother, Cal. Be it the case, he is free to work under the Meteors. However he could also hold a position higher up. I doubt it since he has already been defeated and as such cannot fill the criteria.
Bennet. I know that he has already been defeated, in fact multiple times, but he falls under a complete different category simply due to the fact that he is still evolving. We met him as a nerd, got familiar with his more perverted side, and now he is training as we do in order to acheive greatness, subsidized by El who has connections and pulls strings behind the scenes, helping the boy rise in power and perhaps position. It also fills the criteria, as it has been too long since we fought a bug expert, so he is quite probable.
Laura is actually absent from the story. We met her at the Tanzan cove and first learned that she used to have an E4 position. Given her Grass types, she also fills that role with her weaker same-type-leader being Flobot, the 2nd leader. This however cannot end up as a motiv, therefore her removal from E4 seems actually right. Actually if you choose the dialogues that end up with HER being kidnapped, she disappears again. That was Laura for you.
So far we have
Champion: Solaris - powerful sandstorm team
E4(1): Anna - psychic team
E4(2): Elias - normal team
E4(3): Bennet - bug team
E4(4): up to thought / possible candidates: Heather(dragons, just for type coverage to make the E4 more difficult to manage), Laura(grass, to deal with a water monotype that can potentially breeze through this E4), Blake(ice, weak type, not giving much help, but he's a bad guy that can fit the role), Heather (if she sports a flying monotype instead)