verbs - "I’ve still berries in the fridge"

There was a question posted on Twitter:

Grammar-expert friends: Help needed! I couldn’t find conclusive answers via google so I’ll ask here: I’m writing some lyrics and I want to say “I’ve still (noun)” - for example, “I’ve still berries in the fridge” - is this grammatically correct? I know “I’ve still time” is common"

I wager it's not, because "still" is attributed to the noun. "I have still berries" vs "I still have berries". In the context given, it seems like it would be an auxiliary verb and not the main verb. Thus it would be a compound verb when used in a complete sentence. "I have still got berries" where the main verb is the past participle, "got".

So is it grammatical?