Hi all!
As I wrote NTC is unusual. It is based on principles and few exclusions - only if some principle lead to nonsense. It is hard to understand it, but easy to remember. NTC is not relay system, it will not lead you to right contract automatically! It give you more choices than natural system, for example you can open 1DI/CL with bad 5 major without problems later in bidding.
Hi Ben! My bids:
North
S AK7
H J97
D KQT83
C Q8
South
S J3
H AKQ4
D 96
C KJ654
North South
1D 2C
2D 3CL
3DI 3HE
3NT Pass
2C was relay, showing 12+ hcp, game forcing (after hand evaluation 12-13HCP can be reduced to quasi game forcing).
2D denied a four card+ major, denied max good C/D two suiter, and denied good 6 card or longer diamond suit.
3CL: start for bidding stoppers game forcing without slam interest. 2NT is possible bid - 14HCP, but slam is unlike, need to choose game, so 3CL is right bid. If you will pass max answer 3NT to relay, why you just not shoot 3NT directly?
3DI: stopper+DI, missing stopper HE or SP
3HE: stopper HE, missing stopper SP
3NT: stopper SP
If missing stopper, then start to search best suit for game. Game forcing, because with quasi game forcing instead of 3CL you must use 3DI (3 in opened minor). Example without stopper SP:
North
S 742
H J97
D KQT83
C AQ
South
S J3
H AKQ4
D 96
C KJ654
North South
1D 2C
2D 3CL
3DI 3HE
4HE (3 cards) Pass
Finally Nort hand is worth 1CL opening (15 good HCP, balanced distribution).
So right bidding by NTC must be:
North South
1CL 2CL
2DI 3DI
3SP 3NT
Pass
2C was relay, showing 12+ hcp, game forcing
2D denied a four card+ major, denied max good C/D two suiter, and denied good 6 card or longer club suit.
3DI: start for bidding stoppers without slam interest.
3SP: stopper SP, missing stopper HE
3NT: stopper HE
One of NTC tricks is sometimes is possible to switch who make relays and who answer

. "Slams from planet Mong" hand from Luis.
North:
Axx
KQx
Jxx
9xxx
South:
KQxxxxx
xx
-
AKQT
"Science" way:
South North
1NT 2DI
2SP 2NT
3CL 3DI
3SP 4CL
4HE 4NT
5CL 5DI
5SP 6SP
1NT 1RF, 5 losers or less, with 14 hcp, you need 3 losers or less
2DI showed 6+hcp and denied 4+ major or good 6+ minor
2SP 5+SP, denied slam interest or very unbalanced
2NT 10+HCP, relay!.
3CL singleton/void DI(not min, because 2SP rebid=min)
3DI 12+HCP, relay, show slam interest (hand evaluation)
3SP 4+CL
4CL NAB, begin scan for AKQ and void (SP,CL,HE,DI)
4HE C SP, 0/AK CL
4NT next NAB
5CL 0/AK HE
5DI next NAB
5SP: void DI
Second choice: most simple, but less accurate auction:
1NT-2DI
2SP-3SP(fit,not min)
5DI: ERKCB-5SP(1-4)
6SP
Third choice: not so simple, more accurate:
1NT-2DI
2SP-3SP(fit,not min)
4CL(cue)-4HE(cue)
5CL(odd KC,void DI=KC p denied DI control)-5HE(KC enough for slam, missing Q SP trump)
5NT(Q SP, allow to continue for grand if enough KC)-6SP(KC not enough for grand)
Misho