Who killed General Farnsworth Armstead?

Hint 1 of 7:

Start by ruling out suspects who have an alibi or don't have a motive.

Hint 2 of 7:

No one involved with the Polar Star Diamond can be guilty; Armstead was
dead when Rostov arrived, and Carson Cabot was at home all morning.

Hint 3 of 7:

You can also rule out Lord Fitch; his wife was sick, and he stayed with her.

Hint 4 of 7:

Booth Lacey was at St. Mary's, Wentworth Cobbett was writing, and none of
the Tontine survivors had a strong motive to kill Armstead.