Since augments were first introduced, SE has clearly played with a few processes to make the repetitive process be less-cumbersome.
The best implementation, in my opinion, is Reisenjima augments involving Fern and other stones. You trade all your stones, you augment and you can repeat this process until you get a satisfactory augment.
With the Ambuscade system, you trade your cape and an augment item and choose your path (this is fine). You then have to trade your cape and each successive item one at a time. I've tried trading the cape and multple of the same material and 1 each of different materials. It still only upgrade 1 rank of 1 path. This makes for a total of 50 trades for one cape.
The taru knows how many more times the upgrade can be done, so I would really love to see SE let us store the items with the taru and upgrade several steps of a slot at a time, or at least a menu like Reisenjima where you can upgrade and immediately tell it to upgrade again.