Information that I have been able to find indicates that SS REDSTONE arrived in New York on 23 June 1945 from Swansea, England, and was expected to sail on 25 June to Port Arthur, Texas, and onward from there to Balboa, Canal Zone. Since Balboa is at the Pacific end of the Canal Zone, that suggests a Pacific voyage. Another source confirms a 25 June departure from New York. That's all I have been able to find and admittedly it's not much.
The official logs of arriving U.S. flag merchant ships were turned over to the Coast Guard at the arrival port, and then were eventually forwarded to the National Archives and Records Administration regional facility nearest to that port. If the voyage ended in Houston, the log presumably is to be found at the National Archives facility in Fort Worth (see http://www.archives.gov/fort-worth/ for contact information). Archive staff may be able to photocopy information for you, for some fee of course.
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website