I'm inclined to side with you - for one thing the -dus ending points to Latin and old records were typically kept in Latin, the language of the high church, simply because the scribes (clerks) were often clerics of the church or church trained. It was common practice in the Middle Ages, and lasted for centuries, to record a Latin name on the birth or baptismal certificate even if it was never used in day-to-day life or to Latinize names that didn't have an original Latin form. Taking the Latin record-keeping one step further, J doesn't exist, it would be Ilaudus or Ilandus or the convoluted and confusing Iilandus. Also, I've seen very old records where the written G has so flourished a 'tail' that it looks very much like a J. So adding it all up I'd say Gilandus and some clerk doing some freelance Latinizing of Giles, is most likely.
But then to play devil's advocate, you do have the precendent of Iulianus/Julianus/Julian/Jilian/Gilian and the English trial that separated Julian from Gillian. Hard to call without supporting documentation of some kind that would give origin, etc. clues of the babe in question.