You didn't mention trading out of the first round. If we traded down with Houston, for example, and took their 25th pick, it's not unlikely that two of the three- Mahommes, Watson, Kizer- would be available. But, even if we did trade out of the first round, one of those three, as well as Webb, Kaaya, and Peterman would likely be available as late as the third round.
Frankly, I would suspect that trading down would make it easier for us to draft a QB.