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Any way to a grand?

Playing in a local club my partner and I faced a slam bidding problem. My hand was AT85 KQ K72 A843, partner held - AJ873 AQJT98 Q7. Opponents were silent and our auction went like this:

1N 2N 3 3 3 4 4 5 5 6

our NT range is 15-17, 2N is a D transfer, 3D is positive for D, no real agreement about 3 and 3 but assumed control bids, 4 was key card and 5 is specific K.

About a third of the room found 6 and the rest played in game.

In the post-mortem we tried various auctions to see if they find the grand, we even tried a few agreements that we didn't have at the table. Mainly we wondered whether starting with a transfer would work, or whether the void should be shown, etc. Ultimately we found it difficult to locate the KQ.

We were curious if advanced players using a natural system have agreements for the slam bidding that would enable legitimately finding the high probability grand in either strain.

Yes there are methods and here's what they are
It's difficult to legitimately find the grand on this deal

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