I don't see where you have a problem. It's one thing when a star player goes down with an injury, but here you're talking about two catchers with low ceiling value at best for this season. Maybe having to make extra transactions is a bit of a hassle, but it's not as though losing Hill and/or Closser is going to impact your team, is it? You can probably do just as well with a Melhuse or someone along those lines, and someone like that has to be available.
Considering all the HUGE stars that have gone out for extended periods or are gone for the year, this little catching dilemma is the ultimate much ado about nothing.