Even without damage control in civilian standards it's still a very different issue from sinking WW2 era mostly 4000-10000 DWT ships. Germans had working influence exploders by the end of WW2 and still every torpedo hit did not sink a ship. Granted, every ship hit would have to head for repairs.
As for REFORGER, the idea was that the gear of the troops was stationed at POMCUS sites in Western Europe, the troops themselves simply had to be flown by CRAF aircraft into Europe. As for the ships carrying the stuff of US and Canada based units to Europe, they would have been probably fast container ships like Algol-class (whether in USN colours or contracted) with operating speeds of 25-30kts and commercial car carriers with 15-20kts speed range. These convoys would have not been definitely not easy to intercept as even SSN's would have suffered from high detectability and bad sonar conditions when spurting to attack positions.
In addition, when planning Battle of Atlantic rerun there's the other problem, as illustrated by Grimm Reaper.