Hi Spirithorse!
I invite you to have a look at the page I set up on facebook (search for “Irish Draught Horse Photo Archive”). You will discover from the many historic photos that there is, and always has been, a huge diversity of type within the breed! This is due to diverse founder genetics, enhanced by regional variations in morphology based on different soil types and farm size, and utilization for purposes other than farming including use as artillery horses and army remounts, transportation, showing, sport horse breeding, hunting, etc. There are cobby types, medium framed sporty types, tall scopey hunter types, heavy framed drafty types, and everything in between. None of these types are more or less “traditional” than any other as all of them have existed since the earliest origins of the breed.
You inquired about underrepresented bloodlines…one of the rarest sire line branches in the breed happens to have its sole representative in the USA. Moorpark Image, who stands at Abbeymoor Farm in Sanford, North Carolina, is currently the only approved Irish Draught stallion in the world from the Gortlee sire line, which is one of two sire line branches descending from the very first registered Irish Draught stallion on record, Comet. The other stallion from the Comet sire line descends through the stallion Merrion. This is Silver Laughton who stands in Ireland. In case you haven’t already discovered it, there is a great pedigree database maintained by the Irish Draught and Sport Horse Society of Australia.
Good luck and have fun with your research! There are loads of great resources out there. Can’t recommend highly enough that you go and see as many different horses as possible. Like elsewhere in the world, there is a huge diversity of Irish Draught types in North America. Most of the breeders are very generous with their time and it would be well worth yours to visit them 
Best wishes,