How can I mount cabinetry to metal furring strips with shallow depth?
I usually use cement anchors. There are several types. Hammer-set are like a nail--you push them in through the support into the cement, then use a hammer to drive a pin in the center that causes the anchor to expand. They're quick and  easy but not easily removable. 

Another type of expanding anchor is referred to by a brand name Red Head. Drill similar holes to the hammer-set, but with this one the sleeve is pushed into the hole and a bolt is tightened, causing the expansion (the bolt holds the support in place). If you want to remove this type of anchor, remove the bolt and the anchor can be pushed into the hole. 

These are the 2 types I use the most often and neither requires the wall to be opened. Both are many times stronger than toggle bolts.