Dutch gag actually can take the head down and in, so not ideal for all these strong cobby types!
Cambridge gag works much better, if used with two reins. Tried and tested on half-Suffolk Punch heavyweight cob
Running gags are the most effect at raising the head
Its also possible to lift the head with a jumper bit / UK style tom thumb (aka Junior cow for the USA)
Waterfords do not raise the head and a universal is the same as a continental gag, first action is to raise, second action with stronger contact lowers it (that's why some say it raises and some say it lowers - but are right, but depends on how strong you are pulling)