Cervical cancer is a leading cause of cancer mortality, with approximately 90% of the 250,000 deaths per year occurring in low- and middle-income countries (LMIC). Secondary prevention with cervical screening involves detecting and treating precursor lesions; however, scaling screening efforts in LMIC has been hampered by infrastructure and cost constraints. Recent work has supported the development of an artificial intelligence (AI) pipeline on digital images of the cervix to achieve an accurate and reliable diagnosis of treatable precancerous lesions. In particular, WHO guidelines emphasize visual triage of women testing positive for human papillomavirus (HPV) as the primary screen, and AI could assist in this triage task. Published AI reports have exhibited overfitting, lack of portability, and unrealistic, near-perfect performance estimates. To surmount recognized issues, we implemented a comprehensive deep-learning model selection and optimization study on a large, collated, multi-institutional dataset of 9,462 women (17,013 images). We evaluated relative portability, repeatability, and classification performance. The top performing model, when combined with HPV type, achieved an area under the Receiver Operating Characteristics (ROC) curve (AUC) of 0.89 within our study population of interest, and a limited total extreme misclassification rate of 3.4%, on held-aside test sets. Our work is among the first efforts at designing a robust, repeatable, accurate and clinically translatable deep-learning model for cervical screening.