WHen you have a horse whose heels tend to run forward, I find that often times the bars are left a tad long, or cut too short to support the hoof. If too long, the quarters mash out and flare, and the heels crush. If too short, the foot in motion bottoms out farther than it needs and not only crushes the heels,but bruises soles.
Also, I find that underrun heels are more prevalant on long toed horses. SOmetimes the toe appears short, but a more aggressive bevel may be all that's needed to reduce leverage on the hoof capusle, and reduce the forces pulling the heels forward. The beveled toe will ease breakover for that tendon, as well.
Look at his hairline. Does it bow upwards in the quarters? That would indicated excess quarter length, and that can cause the heels to curl under and mash flat. "Scooping" or "floating" the quarters can alleviate it, relax the hairline, and let the heels straigten up. This is esp true in shod horses.
Even with a bowed tendon, I would avoid wedge shoes. THe under run heels indicate a hoof imbalance that a wedge shoe can't fix. The strong toe bevel will provide the same amount of relief in the breakover and you don't want to raise the heels for long, as the tendon can heal back too "tight". Just don't whack off the heels. Try the "toe bevel, trim the bars a tad, and scoop the quarters" would be my suggestion, but is hard to say over internet, so this isn't a rock solid guide, just general tips based on what my *usual* experience is.
The flat soles indicate to me, the excess length at the quarters and toes.