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That seems right.
I suspect the other one also involves cutting off final letters…
AR(m) + GON(e).

Thanks both

13d. Battered piano, missing note, embodying something obliterating musical form
OPERA SERIA

5d. State of second collection of books with stories
MONTANA

3d. Man with fair promotion prospects given hand by Pole
PASSED PAWN

Parses for the above please.

13. PIA(n)O* around ERASER

5. MO (second) NT (books) ANA (stories)

3. In chess a passed pawn has no other piece preventing its opportunity for progression, hence man with promotion prospects.

PASSED (given) PAW (hand) N (pole)

Thanks for the parses...I still don't understand the "ANA (stories)" in the MONTANA clue.

It crops up now and again, here’s what Chambers says…

aˈna
plural noun
A collection of someone's table talk or of gossip, literary anecdotes or possessions

Thanks Jono, I'd never heard that word before.