What is the extent of difficulty that indicates a lack of goodness in a matter after performing Istikhara, and should one stop at slight difficulty, or continue until completing the matter becomes impossible?

What you mentioned—that a feeling of ease in one's chest regarding a certain action is not a definitive proof in istikhara that Allah has chosen it—is the preponderant opinion. There is no limit to difficulty such that if a person reaches it, it would be considered evidence that goodness lies in its absence. Rather, the one performing istikhara proceeds with what seems apparent to him in his affair. If what he intended is made easy for him, then good lies in that. If it is not made easy, then good lies in being diverted from it, as Sheikh Ibn Uthaymeen said: "If something is decreed to be for him, this is evidence that Allah Almighty chose for it to be. And if he is diverted from it by any kind of impediment, it indicates that Allah Almighty chose for it not to be." So, as long as you have commenced this work, seek Allah's help, rely on Him, and do not despair. And consult people of advice and sound judgment.