I couldn't do it without relays.
It's one thing to upgrade from 14 to 15 but upgrading to 16 is something I wouldn't really ever do. Not to mention that south hand is actually pretty crappy for quantitative with his 4333 shape. I think I wouldn't even bid a quant opposite 14-16NT with that.
To show how it can "easily" be done with relays:
1
♣ - 1
♦ (Nat or 14-19 bal/ Transfer walsh)
1
♥ - 1
♠ (14-16 bal or 3
♥ / Nat or GF relay)
1NT - 2
♣ (14-16 bal without 4
♠ / relay)
2
♦ - 2
♥ (5
♣ / relay for rel points, not interested about doubleton)
2
♠ - 2NT (8 AKQ pts / relay)
3
♦ - 3
♥ (0/2 Kings and 0/2 of top 3 in clubs /relay)
4
♣ - 4
♦ (1/3 in hearts and spades, 0/2 in
♦ / relay)
4NT - 6NT (
♣J and
♥J / just what I needed)
Just a note that if north's other J was in spades, I'd end up in 5NT, nice to have those T9 of clubs so there's no risks