Should I pray at home more often in order to have more time to make Dua during Sujood, as compared to praying at the mosque where there is less opportunity for Dua due to the Imam's speed?
Praying in the Masjid and with Jamaa’ah (congregation) has greater reward than praying alone at home. This is in the obligatory Prayers, but performing recommended Prayers at home is much better than in the Masjid. While you perform recommended Prayers at home, you will have full chance to do long Sojood and recite long Du’a. So, kerfirn your obligatory Prayers in the Masjid and your recommended Prayers and supplication and worshipping at your home.
Wassalam.