Hmmm.. it doesn't sound like the agent tried too hard to find connections on another carrier (Air NZ? Qantas? Via Hawaii??)

Once I helped a couple navigate DTW as they ran for a NW NRT flight, connecting on to TPE. The gate had just been pushed, but the agent gave them the option of staying the night in DTW, or leaving 2 hours later via AMS on KL. They opted for the KLM flight.

Point: I'm a firm believer that there's always some connection (with availability) if you look hard enough. It sounds like your agent didn't look that hard. Sorry you had to spend an extra day in MIA--- although there are lots of _worse_ places to be stuck for a day!!