cURL stopped working after server software update -- 2

We have an EC2 Amazon Linux server with AWS. About a week ago we did a software update in which both curl and openssl were updated, and something happened to break our curl in a couple of our PHP SDKs, the one for Mandrill and the one for Facebook. It also affected one for AWS S3, but we found a fix for that which made it work. Although curl on the command line still works, the curl_exec command in the Facebook and Mandrill SDKs produces a CurlException error code 77, "error setting certificate verify locations". Doing a curl_getinfo after the curl_exec calls shows that the value for certinfo is 0, which seems to confirm that this is a certificate issue. We've verified that we can read our certificates from a PHP file using file_get_contents, so permissions don't seem to be the issue. We've also updated the certificates to make sure they're current. We tried setting CURLOPT_SSL_VERIFYPEER to false in the curl options, but this did not help. We tried setting CURL_CAPATH to the directory where the certificates are located, and this also did not help. This project is being reposted because of the additional information discovered, although many of the bidders on the original project will likely be well suited to this one as well.