Some folks DO bypass the rein rings (terrets) on the hames and also the shoulder strap of breastcollar harness. They might run the reins UNDER the shoulder strap on breastcollar harness. This setting keeps reins from looping out to snag a shaft and allows much rein slide/movement up or down to go with the bit of headset. Seen more with very low headed horses. Folks DO always run the reins thru the terrets on the harness saddle.
You have to look at the horse being used, what is the line from mouth to hands on driver? Conformation, taking into account what stage in horse training he is at. Often a horse will have a low head carriage, so using the rings on shoulder area makes the rein line, (bit to hands) break in too many places. Gives horse wrong signals, pulls him wrongly from what your desired head carriage would be when he is finished developing. You want as straight a line as possible, less drag on his face in taking him up or releases.
I would think your larger horses would have their heads naturally carried with bits even or above the line with reins, bit to hands. Higher set neck would allow them to get a horizontal nose, move “on the bit” rather easily, still keeping the rein line rather straight. Shoulder terrets of buggy hames would be right in line with saddle terrets.
If you are looking at Pleasure Driving, there are nuances with certain kinds of hames. If I have the correct hames in my mind, with the hook bottom, chain between, I think that is for Gig Harness use. Special dress-up harness, not a common hame. Out of place on less formal vehicles. I use the Mischka Calendars as a good reference, AND found on line!
http://www.mischka.com/shop/product.php?productid=16674&cat=0&page=1&featured
Give it a minute to load all the photos. There is a Unicorn of light horses, with Leader wearing the hames I am thinking of, but Turnout is a Formal vehicle and people and horses are dressed to suit the vehicle. Horse is wearing a correct, SPECIAL saddle for a Leader. He could also be a correctly turned out, Tandem Leader with a Wheeler and fancy Gig behind him. Gig is also very formal when turned out correctly.
Just some of those picky details from Traditional turnouts in the past. The ADS rule book has much information about what is correct harness, bits, hames, to go with various vehicles, as you look at classes to compete for Pleasure Driving.
Runabout harness is not suitable for Gig horse or Tandem horses. Like your draft hitch, best show harness is not suitable for a Marathon vehicle at a CDE, just in the wrong setting.
There is a “language” of horses, harness, vehicles, and what goes together correctly. The knowledgable viewer will see MUCH and deduce more, just by looking at the Turnout as it goes by. Seeing if you mixed styles, went for total correctness, or have just come to drive around. The “silent appraisal” of people meeting unknown people in a new setting happens all the time. We all do it as we go out to play. Could be Draft folks, steelworkers, fishermen, cowboys or Rodeo cowboys, checking each other out to reach a conclusion about how “real” or knowledgable the others are in this skill area. I know I always check out the cowboy hats, see the creases and brims, because “real” cowboys treat their hats a certain way. Visible when you look at them. Knowing and observation of situations, people, keeps you from harm in many settings.