Juvenile Collared Crows have the white collar (although sometimes greyer/browner than adults), so if they lacked the white collar they weren't Collared Crow.
I have seen House Crow at Mai Po and Pak Nai in the NT, but they are unusual. They typically look structurally like Large-billed though, including the bill shape. On a good view you may be able to see the greyer body, and they often also look noticeably small compared to Large-billed/Collared.
I think it's most likely that your birds were juvenile Large-billed (which can look slightly smaller-billed than adults) but House Crow may still be a possibility.