Finding Medina

Before Father Miguel Hidalgo was captured by Royalist forces in March of 1811, he commissioned a modest but vocal supporter from the Rio Grande Valley as his emissary to the United States. With a dozen or so loyal followers, that emissary - José Bernardo Gutiérrez de Lara escaped Royalist capture and crossed over the Sabine, where he would spend the next two years rallying recruits and resources to the cause of Mexican independence. Multiple contemporary accounts of the Battle of Medina relate the Republican army's route to the battlefield. Unfortunately, they almost all relate it differently or contradict each other in some material point. Despite their contradictions and ambiguities, what details might they have in common?