Answer:
Option C is correct: messages, SETI is the most heavily funded project of its kind, yet the search for extraterrestrial life will likely be
Explanation:
Option A is wrong because the modifier was wrongly placed and the search cannot be recognized as a project.
Option B is wrong because it failed to use simple future tense when describing the likely outcome of the search "yet the search for extraterrestrial life would likely have been "
Option C is correct because it uses the simple future tense as described above "will likely be"
Option D is wrong because it is the search that would be stymied and not SETI and also did not use a simple future tense
Option E has the same error as B as it failed to use simple future when describing what will happen