I agree that those variants are possible, too. «Незаба́ром» sounds especially natural.
I personally wouldn't use «шви́дко» and «би́стро» in this sense, but the dictionaries have those meanings so perhaps they are possible, too.
Why does Duolingo have скоро (soon) and пізніше (later) so far into this course? They are very common words and should be introduced earlier in the lesson plan. As a former English tutor, I used to introduce these words early on in reading and writing lessons because of their common usage.
If and when revisions are made to the lesson plans for Ukrainian, I think the concept of learning common words early on is one which should be considered as important to help students to feel as if they are beginning to grasp the vocabulary.