Double shot ?

West
AJ4
J842
K874
106
North
109762
109
AQJ103
K
East
Q
KQ7653
5
A9872
South
K853
A
962
QJ543
W
N
E
S
P
P
P
1
X
3
3
P
P
4
?
D

North ask what was the meaning of 3D, East reply is "natural" (after some hesitation).

Let's assume that after west 4H north correctly guess that west 3D was probably artificial so he ask what system they play and the answer is bromad and after another question we learn that 2C/2D/2NT/3C are all raises 2= (construc 3 card) 2= (limit 3 card) 2Nt= (limit 4 card) 3 = (constr 4 card) but 3D is natural (and indeed that what's written on the CC/notes) so north is correctly guessing that west got a constructive raise rather than a limit raise. Both North and south expect that the director wont allow 4. Do you feel north should bid 4S even without EW infraction ? Can north bid 4S as a freeroll/double shot ? What about south ?

edited ..I now think that east had the T of diamond singleton, also funny i was south lead my ace of switch to a (couldnt read the 9 from T9) declarer played the A pull another round of trumps T-K-A-low.   Than low , low, 6won the trick. 4H+1 5 rollled back to 3S+1 for NS.