Find one with clearly defined gaits and there is no reason what so ever why you can't be placed. 4 gaited are normally clearer than a 5 gaited.
Al, next time Nev comes over, come with her and meet our guys

We dressage 3 out of the 4 of them. Admittedly only unaffiliated, but thats because it's local. With a lot of lessons the mare could affiliate. Currently on my wall I have a 3rd and a 4th from dressaging icelandics. If the horse is going correct and produces an accurate test then the combiantion should not be marked down. Icelandics only look lame when they become 4 beat, or go into piggy pace. The only prejudice you can get is the "adults on ponies" prejudice. The judge at my last competition adored the little gelding. Because he's accurate and sweet. We don't work in an outline, which is why we didn't win. But he's responsive and off the leg. None of ours have a hugley flamboyant action.
I'm going down to London on wednesday to have a lesson on the mare with a classical dressage trainer down there (my 18th birthday pressie) I'll arm my normal instructor (whose treating me) with my camera and make sure I get loads of pictures to show you!
For the record, get an icey at World Championship level (

) and they have more movement than most things at elementary, harnessed into dressage rather than competition (which obviously with this kind of movement is a breeders first priority) then there would be no stopping them!