The foot looks interesting - can you post a photo of the pattern on that please?
The pattern looks like a daisy and button type pattern, which is often seen as pressed glass. The shield shapes are seen on many cut patterns. Thinking out loud here, I'm wondering if it's a hybrid of pressed and cut glass, if that's possible?
Have you checked the base for an acid etched mark? Sometimes these are feint and hard to see, especially where the base has been cut, but if you look closely using a magnifier in good light you may spot something - even if it's only a part-mark it may offer a clue.
It might also be helpful if we modify the subject of the thread for you to attract the attention of the cut glass people?