A Dutch 'Gag' is not a gag at all. Gags lift the head, whereas 3-Ring, 2-Ring or Single Ring (Pessoa) bits of the Dutch Gag type apply strong poll pressure by rotation of the large ring. So they lower the head, not lift it.
'Elevator' bits are supposed to lighten the forehand, which they do by forcing the horse to raise its head and neck.
The idea of both these bits is that once the horse becomes used to their action (ie. The rider gives when the horse responds correctly) it should be possible to dispense with them. However, horses get excited when jumping and galloping: they forget things, or think they know best - I'm sure we've all been there. You have to be able to stay in control or you become a danger both to yourself and others.
So keep on with the schooling, but if you need a stronger bit in more stressful circumstances then use one. In an ideal world we'd all be using rubber snaffles and cavesson nosebands, but that's not real life :)