What version of Quartus? I've had very good experience with it replicating registers into the OE(with recent versions of Quartus, but I mean within the last 4 years or so, so it's been working for a while). I usually just do I/O timing constraints and it does the replication for me, although Fase OE Register assignments should work too.
If you've already replicated it though, that definitely should work. What assignment/constraint did you put on to stop that from occurring? Can you show the syntax? (It can be done in HDL or assignments in the .qsf, so a few ways to go about it...)