Relying exclusively on radio communication, both to transmit messages it has encoded and to receive messages, the search for extraterrestrial life by SETI, the most heavily funded project of this kind, will likely be stymied if this form of communication does not yield any tangible breakthroughs.

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