A 42-year-old woman with asplenia (post-splenectomy for hereditary spherocytosis 5 years ago) presents with a 2-day history of high fever (40.2°C), severe headache, neck stiffness, and photophobia. On examination, she has a petechial rash on her trunk and positive Kernig's sign. CSF analysis shows: protein 280 mg/dL, glucose 18 mg/dL (serum glucose 95 mg/dL), WBC 1200/µL (92% neutrophils), Gram stain shows Gram-positive diplococci. Blood and CSF cultures are pending. What is the most appropriate immediate antibiotic regimen?