It seems to me more a question of how to write in an attic style ("Characterized by purity, simplicity, and elegant wit"). The challenge is to find a workable compromise, so as to be both sparse and easily understandable -- using the specific tools of the language you are using. In practice, there is no set answer, though there are "tips and tricks" that could work, or not work.
The problem of the sentence:
Only then does an informed review of existing and the careful design of new solutions become possible.
is that your interlocutor has to "skip an oddness": the adjective "existing" has no substantive attached to it. They would then have to parse the next five to six words before they make sense of the sentence. There is also the risk of ambiguity, or at least of being misleading: my spontaneous reaction was that "existing" was perhaps used as a substantive like French "l'existant", so I missed your meaning; then I had to recognize my error and work it back.
German has a syntax that does this kind of thing frequently (especially sending verbs at the end of the sentence), so people are not averse to it. At the same time it has well inflected conjugations, as well as cases for nouns, to keep you on the right track. By contrast, English tends to work the other way, by "building up" the meaning progressively, from left to right; furthermore, its nouns, adjectives and verbs have little inflection, so it is easier to be ambiguous (to avoid ambiguity, the customary position of words in a sentence plays an important role). For these reasons, I would try to avoid unusual constructions, especially when they create a "suspension of understanding".
To solve this issue, you could perfectly repeat yourself as you proposed; that would be explicit (this tends to be better accepted in scientific and technical subjects, but could be frowned upon in humanities).
Here is what I would do, to respect all these constraints:
Only then does an informed review of existing solutions become possible, as well as the careful design of new ones.
This might not be the purest construction, but it would work.
