Showing gratitude for omiyage yet to be completely finished (ごちそうさまです？） Can I say if I want to show gratitude for edible omiyage I’ve received but have yet to finish? For example, I received a box of cookies recently and want to say thank you as soon as possible, rather than after I’ve finished the whole thing, in which case I’d say . Does accurately express this or is there a specific phrase for this situation?

If I understand your situation correctly, you received the omiyage, ate a couple of them and will be meeting the person that gave them to you before finishing them all. As naruto has answered is the normal response.
As far as adding or something, whether you use past tense or present depends on what you want to say.

could mean that you have had that kind before and think that it is really good, or that it is the first time you had it and were surprised at how good it was (level of surprise perhaps depending on emphasis when said). You would need to add more information to differentiate between these two meanings. In this case, whether you had one or finished all of them is irrelevant.

While using the past tense would refer specifically to the ones they gave you, and not that brand or kind of snack as a whole. This sounds more like you finished them all, but that does not necessarily have to be true.

Note that I'm just using because I don't know what it actually is.