For Acol, if playing a basic system, the bidding could go something like the following:

N.      E.        S.       W

          -          1     -

2    -          2     -

4N     -          5     -

5N     -          6     -

6   -           -         -

where:

4N     -    Roman Key Card

5   -     2 Keycard and Q

5N    -     King ask

6  -     No non key card K

After the 2 rebid the leap to 4NT is a leap of faith hoping South has some support of the  suit. North hits the Jackpot but with very little knowledge of South’s distribution can’t push on to the Grand Slam.

For Acol, if playing a Jacoby 2NT, the bidding would go something like this:

N        E          S         W

           -          1       -

2N      -          4       -

4N      -          5       -

5N      -          6       -

7

where:

2N    - Jacoby 2NT (version where 3 level response show 5 card suit, 4 level show singleton/void)

4   - 5+ 0 - 1 denies a 5 card side suit

4N    - Roman Keycard

5  - 2 key card and Q

5N   - K ask

6  - No non key card K

Now North after using the intermediate Jacoby 2NT has gain extra distribution information and knows there  is no possible  loser and can count 13 tricks by either clubs breaking  if South has 3 or 4 or South being able to ruff  with the extra  length they must otherwise have to set up remainder of suit. However, without knowledge of the Q it is difficult to chance bidding 7NT.

For basic Precision, the similar bidding would occur except by playing 5+ card major openings in the first bidding sequence North would know South had 6+ which would give more confidence to bid 4NT directly.

For Precision playing a Jacoby 2NT and 5+ card majors, some pairs reverse the level of bidding so 3 level bid would show a void or singleton and 4 level a 5 card side suit.

Playing our loser based system, Imperspicuity,  these hands are also challenging. Our bidding should be the following if there is no opposition bidding:

N.      E.      S.        W

          -        1      -

1    -        1      -

1    -         2     -

2    -         3     -

3    -         4     -

4N.     -         5    -

5    -         6    -

6    -         7    -

7N.    -          -        -

Where:

1   -   <= 6 L 0 - 37 HCP any shape

1   -   >= 9 L or <= 8 L 4M unbalanced

1   -   5 L or <= 3L any shape

1   -   >= 10 L or <= 8 L 4M unbalanced

2   -  5L 5+

2   - shape asking relay 10 L or <= 8 L 4M unbalanced

3   - 6+ 3+

3   - shape asking relay 8 L 4M unbalanced

4   - 64 9 total losers

4N.   - CROSS 

5  - 2 keycard same colour

5 - CROSS continuation Ask for K

6 - No K

6 - CROSS continuation Ask for Q

7 - 2 Q opposite colour/rank

7NT - to play

North has a 4 modified loser hand and after the opening 1 opening using the rule of 18 North already knows there is a possible Grand slam if a fit can be found. As 1 response would show a 5+ positive response North must wait for South to reveal their hand with a waiting 1 response. Once South shows a 5L 5+ suit and a fit has been found North takes over captaincy and asks for shape to eventually determine South’s total losers which proves important to be able to bid 7NT Grand Slam.

From Law of Total Losers North, by subtracting South’s modified losers from the total losers South has, knows they have 4 - 5 cards higher than a J. When later A & A are revealed, no K, and 2 Q for South to have 5 losers that they must have 3 and so their 2 Q of opposite colour/rank are the Q & Q and South has 643. 

Therefore, provided  break no worse than 3-1 then North can count 14 tricks in NT and bids 7NT. 

North can technically bid 7NT after the 6 response as North knows at this point South has 3 and at least 2 Q to have 5 L. They would have to rely on either  breaking no worse than 2-1 or  2-2 if South had only 2 Q including the Q.

Last year I was reading a book from the 60's by Rixi Markus. She discussed the natural use of the 2♣ opening calling it CAB (Clubs, Aces, Blackwood)

There are two types of 2♣ Openings. Either a strong unbalanced hand or a strong 23-25pt hand with balanced distribution. The 2♣ Openers rebid will clarify which type.

A 2♣ Opening bid asks responder to bid the suit of any Ace that they have.

Response's to 2♣ are:

2♦ = Less than 8 points, NO Aces.

2♥,2♠, 3♣,3♦ = the Ace of that suit!

2NT = 8+ points, NO Aces.

3NT = 2 Aces

4NT = 3 Aces

After a double negative response from advancer, 2D then 2NT, advancer can pass below game level if Opener rebids his suit.

We adopted it and found it very sucessful.

The bidding in our action would have gone:

South   North

2♣        3NT*

4♥*       4NT*

5♠*       7NT*

3NT shows two Aces

4H shows a strong unbalanced hand in hearts

4NT RKC

5♠ Two Key Cards with the Queen of Trumps

7NT Yaa! I must pick up a lotto ticket on the way home.

As a footnote although E/W is Vul, I would have opened East's hand 2♦ He has only

If East opens a vulnerable weak 2 then bidding a Grand Slam is more difficult. It is important to have a prepared defence. We play a natural 2NT (5 loser 0 - 25 HCP) any shape that doesn’t promise a stopper and invites partner to pass if they have >= 11 losers 4333 shape and 2 stoppers in . The advantage of this bid is that using the rule of 18 it gives partner an immediate indication of the bidding level possible if a fit can be found. In this case a Grand Slam is indicated as being possible.

So bidding would go something like:

N.        E.        S.       W

           2     2N.      3

x.         -         3      -

4N       -         5      -

5      -         5      -

5N      -          6       -

6      -        6       -

7      -        7N.       -

-          -

Where:

2 - weak 6+

2N. -   5 loser (0 - 25 HCP) natural N

x.    -   <= 9 loser 4M unbalanced.

3 - competitive raise

3 -   Shape asking relay

4N - 4 <3 4 loser (we play a rolling loser showing response: 3N 9 L, 4 8 L, 4 7L etc)

5 - CROSS

5 - 0 or 3 key card

5 - CROSS continuation

5N - 1 non key card K

6 - CROSS continuation

6  - 0 or 3 Q 

6  - suit of K query

7 - K

After North shows 0 Q South can deduce North has <= 9 total losers (6430, 5440, 7411 etc shape) from the Law of Total Losers and, therefore, from opponent’s bidding North must have 5+4. Provided clubs break south can count 13 tricks in NT and bids 7NT.

Try getting there after:

(2D) 2H (3S) 4D;  3S = fit jump, 4D = H raise
(4S)  ?

FWIW I think that North bypassing primary H support to show a C suit is a really bad practice, as they can never know if they've shown a forcing fit afterwards, and it leads to lurching auctions like your jump to 4NT.

The main benefit of playing jacoby is that you don't pre-empt yourself on your slam boards. Having a relatively poorly defined jump to 4D after a 2N response really crowds the auction.
Instead if South was able to bid 3S to show extra values (the void, two aces, and a 6th trump) and a D shortage - North could evaluate that Axx opposite a singleton/void is great; the source of tricks in C is great; the spade control is great; the good trumps are great; etc.
That gives you more bids (3N, 4m) to make to initiate a more descriptive cue-bidding sequence and would benefit any pair looking to accurately bid grand slam.

If East opens a weak 2 with a 3 response from partner to show a fit jump then that makes the bidding  more interesting:

N.      E.      S.      W

         2   2N.     3

x        4   -         -

4N       -      5     -      

 5     -      6     -

7      -       7    -

-           -

Where:

2 - weak 2

2N   - natural no trump as previously defined (5 loser 0 - 26 HCP)

3 - fit jump

x     - positive response 4M

4 - fit raise

4NT - CROSS 

5 - 2 key card same colour

5 - CROSS continuation Non Key card K ask

6 - 0 or 3 

7 - pass or correct

After EW agressive bidding showing double fits in  &  from the rule of 18 North knows NS can ‘make’ 15 tricks in either  or  and South has a shortage in  so looks for slam. After 6 response South has <= 9 total losers and 2 or more Q.