Is there anything objectionable (in terms of halacha, hashkafa and middos) to using the Ferber method for training an infant to fall asleep on its own? There is an element of cruelty, and the ultimate benefit is probably more for the exhausted parents than for the child.
As I see it, this question must be divided into two separate issues:
Let's start with Issue #2, as it seems to be more at the core of your questions:
As far as I know, no traditional Torah sources discuss this particular issue of letting a child cry it out for the purpose of "training" the child to sleep. I don't believe this to be a function of "the Torah opinion" taking sides on the issue of whether or not sleep training has a negative effect on a child's development, it is more likely a function of the fact that the concept of sleep training was only introduced in the late 1800s and was only popularized in the subsequent decades.
If it is indeed true that "sleep training" a child improves their self-esteem, intelligence and trust in their parents (and by extension God), then I think we can all certainly agree that Judaism would not take issue with, or perhaps even encourage, such a regimen. However, being that there is conflicting evidence, leaving the answer unclear, we should probably act as we would with any safek (doubt in Jewish law), and stand on the chazaka (status quo), until there is substantial evidence to uproot this status quo (the status quo is probably, as my wife points out, somewhere in between the two methods, parents making decisions based on their child's needs using their intuition and parenting style).
Decisions such as these should be made based on a parenting style, which Torah sources do comment on. For example, one piece of Torah advice that comes to mind is, "have the left hand push away and the right hand draw near" (Sanhedrin 107b http://www.hebrewbooks.org/shas.aspx?mesechta=24&daf=107b&format=pdf 5 lines above the start of the mishna in the middle of the line and Sotah 47a), meaning that we should have balance in our parenting, both showing love and being firm. Of course, the "pushing away" is done with the left, weaker, hand. For more on the Torah's views on parenting, I would strongly recommend Zriyah U'Binyan B'Chinuch by Rav Wolbe, which is available in both Hebrew and English from Feldhiem Publishers and Amazon.
Now, onto Issue #1:
Based on the sources listed in the above mentioned article (stories of Mittler Rebbe, Rabbi Yisroel Salanter as well as the undocumented halachic sources) and other sources (http://www.mechon-mamre.org/p/pt/pt0319.htm#16, http://youtu.be/g1123SvR5F8?t=4m20s, http://mechon-mamre.org/p/pt/pt2821.htm#13) it seems clear that it would be detrimental to one's middos/soul/personal growth to stand idly by while a fellow human being, particularly a child is in pain/crying. In certain situations (particularly as parents), however, we must do things which are detrimental to ourselves if they benefit others and therefore if sleep training is shown to be beneficial to our children then we may have to forgo our personal growth for the growth of our children. Being that (as outlined above) this is still in the realm of safek (doubt) we would not be obligated to forgo our personal growth by standing idly by as a child cries unless it is abundantly clear that this would benefit the child in the long-term.
All in all, I think the question you are asking is "Does the Torah/Judaism take sides on the 'sleep debate'?" and the answer is most certainly not. This is scientific question and we must act, as always, according to the facts that we have (or don't) based on the principles of the Torah.
This article from AMI magazine goes through the pros and cons of the Ferber method. http://www.batyathebabycoach.com/wp-content/uploads/2011/05/Ami-Magazine-Article.pdf
Kohelet says, "Spare the rod spoil the child" Sometimes a little pain to the child is necessary for it to properly grow and function and learn to become a great person.
The phrase is generaly understood in modern contexts to be talking about discipline in general and not actual beatings.
However, if you feel that the Ferber method is objectionable to you, then you would be required to not use it. That is, if you think the pain cause to the child is needless and won't actually help them, then you shouldn't do it. But most people believe its beneficial for the child in the long run.