What happens if a double-faced card that is copying a different double-faced card that is part of a melded creature tries to meld?
Hanweir Battlements and Chandra are exiled permanently. The Metamorphic Alteration goes to the graveyard.
As you already noted, only meld cards can meld. You can exile Chandra and the Battlements with Battlement's ability, but those two cards cannot return melded.

701.36b Only two cards belonging to the same meld pair can be melded. Tokens, cards that aren’t meld cards, or meld cards that don’t form a meld pair can’t be melded.
701.36c If an effect instructs a player to meld cards that can’t be melded, they stay in their current zone.

Note that 701.36b calls for meld cards, not meld objects. Being able to meld is a property of the card, not of the object represented by it.