[subject] + 好不容易 / 好容易 + (才) + [verb phrase]
[subject] + 好不容易 + [verb phrase]
好不容易 before a verb says the action succeeded, but only after real effort or a long wait. 才 usually follows it, and the result is something that did happen.
The effort often explains what comes next: having worked so hard for something, you don't want to waste it.
Before a verb, 好容易 – without 不 – means exactly what 好不容易 means. The 不 makes no difference here.
After the subject, as the main comment, the two are opposites: 好不容易 is "really not easy", and 好容易 is "so easy". The "finally managed" sense only exists when the word goes in front of another verb.
好 + 不 + adjective as a general frame has its own point.