To answer the question regarding Backhoe vs tools, for me personally it痴 a factor of time and space. These stumps are in my immediate backyard and I知 on a time crunch to get them out in order to grade, seed and a host of other improvements I need to tackle in the next 2 weeks. The backhoe is awesome and I do not regret the purchase. I read a lot of remarks in how it痴 overrated and too expensive and ineffective and I壇 have to disagree. If you need one you need one, and it痴 nice to have anytime I need it. It痴 limited by hydraulic pressure and the weight of the tractor, but it痴 still 1000x better than a shovel. I use it to dig down until I知 hitting a root I can稚 bust through, not to mention my property has ALOT of rock in the ground.
I don't think any of us are trying to discourage you, actually rather to encourage. Using a backhoe (large or small) is more about experience and technique. In the picture of the 24" stump, I may opt to set up the machine with one outrigger barely touching and the other fully extended creating a ~45 degree angle to the stump then dig under the stump to loosen. I would also move away from the stump to where I could rip the roots out, then move in closer to get the extra dirt off. from the picture, any reason not to use the front bucket to help pry out the stump? You might be surprised what the "little machine" can do. Even the biggest ones have to use some problem solving skills to get the job done.