All Praise be to Allaah.
After discussing the question you raised with the learned sheikh Abdul-Aziz bin Abdullaah bin Baz, he has indicated that Islamic shari'ah does not legislate holding two jumu'ah prayers in one place. You should choose the most convenient time--and its timing extends until the 'asr prayer--and urge and enjoin all the Muslims to attend. Note that it is mandatory to stop all work (including attending classes) for the jumu'ah prayer. Whoever misses it would pray the dhuhr prayer.
May Allaah grant you all success in obeying Him and pleasing Him and may He ease your affairs wherever you may be.