Unable to import private key "Error: Subkey 1 wasn't found in public key"

I have a key with two subkeys:
sec 4096R/93484BA9 2013-08-18
uid Robert Diamond rmd6502@gmail.com
uid Robert Diamond rmd6502@gmail.com
ssb 4096R/6357F89B 2013-08-18
ssb 4096R/2AB41216 2015-06-13
ssb 4096R/E8F84991 2015-06-13

When I try to import using the web interface I get the message shown above, before I can even click "upload"
When I try to import using the command line interface (osx) I get
gpg --export-secret-keys -a | keybase pgp import --push-secret
▶ ERROR This key is already active. You can't add it twice. (error 923)

When I try to import the subkeys I get
gpg --export-secret-subkeys -a | keybase pgp import --push-secret
▶ ERROR openpgp: invalid argument: no valid signing keys

Start by reproducing the web-interface failure and the listed `gpg`/`keybase pgp import --push-secret` commands with the supplied key structure. Compare full secret-key and secret-subkey handling; done means the key can be imported without the reported missing-subkey, duplicate-key, or invalid-signing-key errors.

Written by the indexing model from the issue text.