No, the progressive does not signify ineptness. The progressive simply suggests an ongoing action. These tenses don't have a connotation in and of themselves.
I don't think that it's ineptness at play; it's more an indication of the difficulty involved in the task. They have not yet mastered the level of proficiency required for such a transformation, but that's not to say they're incapable of doing so eventually. And none of this has anything to do with a progressive action.
What's tricky is that the action is in the future (it could very well be written as they wouldn't be changing), but the story itself is set in the past.
Before I get further into the grammar, I want to highlight the context that indicates inability, which is not the verb tense:
They were all very impressed and couldn't wait to get started, but soon realized they weren't going to be changing the furniture into
animals for a long time.
It's more that they were so excited to try, but quickly realized the task was more difficult than they'd originally thought, and as a result, they won't be doing it successfully any time soon. That's not to say that they're inept and are incapable of learning.
In that sentence, weren't indicates that it's the past tense, but it's going to be that indicates the action hasn't occurred at this point in the story, and that's what makes they wouldn't be changing semantically the same.
With that said, it's clearly the past progressive tense (weren't changing). Be changing, as you have marked it, is not the progressive. It's actually weren't [going to be] changing.
This is a construction generally found in narratives. It's describing a future action in the past tense. That's why I can easily substitute would for going to. Ordinarily, a non-conditional action in the future takes the modal will. I cannot, however, write will not be without changing the tense (i.e. the tense suggested by the words themselves). That would change the setting to the present.
Since this narrative is set in the past, it's actually saying: Upon discovering the degree of difficulty involved in turning desks into animals, they quickly realized that they would not be doing so any time soon.
If it were set in the present, it'd be more like:
As they watch her change her desk into a pig and back again, they are all very impressed and can't wait to get started; they're realizing, however, that because it's so hard to do, they aren't
going to be changing the furniture into animals for a long time.