While the Alp Trainer Mid can't be called soft, it is still more flexible at the ball of the foot than the Snow Trainer. From Salewa, the two boots that have a support similar to the Snow Trainer would be the Mountain Trainer Mid, or the Rapace. The Rapace is in fact slightly stiffer and can handle crampon use as well. Unfortunately, OMC does not stock either of these models.
Some boots that are similar to the Mountain Trainer/Rapace type that have a good fit record and worth investigating-
Scarpa Kinesis Pro
La Sportiva Trango S Evo
All of these are characterized by having very stiff soles, but with improved ankle flex to allow a less clunky movement. They also have reinforcing features inspired by mountaineering boots, such as full rubber rands. Indeed, the Trango S Evo is usually categorized as a mountaineering boot, but has found great favor with backpackers who are looking for a light, nimble, but stout hiking boot.