In this tournament the fighters start off in combat, and no charge bonuses are counted, so Swiftstride for Maneaters would be useless in this case. You’re right though, in a regular game Swiftstride would be a great choice and would be very helpful for getting that all-important Ogre charge in.
I wanted to see if anyone else had any recommendations before choosing a banner myself, but as nobody has given any recommendations I will make the choice.
The Banner of Eternal Flame is certainly a killer choice to take in this contest - there are an abundance of units with Regeneration or Flammable in this tournament, so Flaming Attacks would cause havoc. However, in an all-comers list it's a lot less likely to appear because the majority of the units in the game either have no special rules that make them susceptible to Flaming Attacks or have an active defence against them. The White Lions in your tourney have the Banner of the World Dragon because that's the most popular build when they are included in a competitive all-comers list, so it would make sense to apply the same rule here. I think the Razor Standard would be of more use to Maneaters in a game overall, because currently they only inflict a -2 armour save penalty due to Strength 5 which gives even regular infantry with heavy armour and shield a 6+ armour save (alongside their parry save). In this tourney it would also give them a bit more oomph against units like Kroxigor and Tree Kin, so I think they should take this banner.
Ironguts can also take a Magic Standard. Again the Razor Standard would help give them some extra oomph in combat in a regular game, but in this tourney it would be useless because the most heavily-armoured units they're going up against will have a 4+ save, which is already covered by their Strength 6 Great Weapons. Therefore, for the Ironguts the Banner of Eternal Flame would be a much more useful choice.