Gabriel Bodard has brought to my attention the Epigraphic Database for Ancient Asia Minor / Epigraphische Datenbank zum antiken Kleinasien. The website is in German and English and contains various Greek and Latin inscriptions from ancient Asia Minor.
They have begun with the Roman province of Galatia – I’m glad to see they got their priorities right! The search fields are quite detailed for location so if you want to see everything that was found at a certain place it is very helpful.
It seems you have to search by exact form. e.g. CRISTOS turns up nothing, but CRISTOU returns 12 results.
Commentary is provided but it is in German, even on the English side.