After I dropped the y2038 code into Time::Local::Extended, a few other authors were asking me to do the same for their modules. Rather than have them all ship copies of the C code and redo the XS work, I've just uploaded Time::y2038, a thin wrapper around the y2038 project.
This means you can use Time::y2038 and get 2038 safe versions of localtime(), gmtime(), timelocal() and timegm(). Also included is Time::y2038::Everywhere which replaces the localtime() and gmtime() functions for everyone. Use it once and your 2038 problems are solved in all the modules you use.
Note that the versions of timelocal() and timegm() are not compatible with Time::Local. Time::Local does some "helpful" things to the year (9, 109 and 2009 are all interpreted as 2009) making it impossible to specify certain years (like year 9). I'll leave it to Time::Local to wrap that bit of stupid around them.