Two-way checkback auctions which show good support for opener's suit

There are a number of popular artificial treatments which can distinguish between invitational strength (or less) and game force strength.  Typically clubs is used to show invitational strength or a desire to set the contract (or play diamonds) while diamonds forces to game.

Examples of these types of convention are game-forcing and non-game-forcing Stayman after a 1NT opening, two-way checkback (or XYZ) after a 1NT rebid (or any 1-1-1 auction), and the Wolff signoff (or adjunct) after a 2NT rebid.  [postscript note: I am only considering auctions where a club bid forces a diamond response, plus the "negative" response to the non-game-forcing Stayman inquiry.  My use of the term "two-way checkback" was confusing because it opened up other possibilities which were not intended.  The form of two-way checkback that I am considering here is the one where 2D is forced.  It's possible that I'm misusing, or even abusing, the term but it is what I play in those partnerships where I can't persuade partner to play the full XYZ treatment]

The sequences that start with the artificial game force are relatively straightforward.  And when responder uses the weaker bid and then invites game or sets the contract also require no comment.

But what about those sequences where responder uses the weaker sequence and then bids game anyway?  For example, using the Wolff adjunct, 1C p 1M p 2NT p 3C* p 3D* p 3NT.  He could have bid 3NT directly over 2NT.  So what's all this dilly-dallying?  He must be showing clubs and a hand that would be interested in slam opposite a suitable hand with good clubs. 

The same thing can be assumed a level lower if the bidding goes 1C p 1M p 1NT p 2C* p 2D* p 3NT.  By the way, all of these 1C sequences would also apply if responder first bids 1D instead of a major.

A similar inference can be made if in either of these situations, the bidding goes to 4M.  This looks like a 6-4 hand with 6 of the major and four clubs (or better) and of course slam interest.

What if opener started with 1D?  1D p 1M p 1NT p 2C* p 2D* p 3NT.  Or 1D p 1M p 2NT p 3C* p 3D* p 3NT.  Responder has slammish values with diamond support.

There are some other sequences after a 1NT rebid.  What's the difference between these two sequences?

• 1m p 1M p 1NT p 2C* p 2D* p 2NT?
• 1m p 1M p 1NT p 2NT?

By general agreement, the first sequence shows five card support for opener's minor, as well of course as the four of a major.  The second sequence shows a maximum of four of opener's minor.