Opener's Checkback?

An auction from BBF that I misunderstood initially made me think in a way that was relevant only in the auction I saw while in my own world.

1D-P-1H-P-
1S-P-1NT-P-
2C?

Obviously, this auction in a natural auction world shows 4144, 4054, or maybe 4153 shape.  However, there might be some cause for using this 2C rebid for a different cause, opting to pass 1NT with the prior patterns.  I mention this not because I think the merits are there but because the sequence intrigues me theoretically.

One plausible alternative meaning is a hand with a diamond rebid but three hearts, maybe 4351 or 4360, to enable finding the 5-3 heart fit that might exist.  Another possibility is to have 2C handle hands where a 3D jump might make sense, to avoid the three-level unless this is necessary.  These could also be somewhat combined, where for instance Responder is free to introduce hearts (or Opener to rebid hearts) when Opener bids 2C, as this wouyld be forcing.  Hence, you could have:

1D-P-1H-P-
1S-P-1NT-P-
2C-P-2H as a fifth heart and acceptance values or

1D-P-1H-P-
1S-P-1NT-P-
2C-P-2D(weak)-P-
2H  as a third heart and maximum values for the sequence.

This might be all the more relevant if the partnership uses Mini-Roman (ugh!), where the 4-1-4-4 or 4-0-5-4 option is already off the table.