How to Export Client Certificate from Firefox for Android on non-rooted device

I had a website install a client certificate into my Firefox browser (v35.0.1) on my tablet and I want to export and backup the certificate. I've found out after the fact that Firefox on android doesn't actually provide any native mechanisms for managing the certificate store (and does not integrate with the Android native certificate store). Additionally, all Firefox add-ons I've found are out of date, preventing them from being installed.

I found an article here that suggests copying the cert9.db and key4.db files to PC and using a third-party application to extract the certificate and key, however this device is not rooted and the file browsers I've tried do not allow browsing the true root filesystem. As a workaround, I tried putting the path to the files in Firefox to download them to somewhere more accessible, however Firefox refuses to download them (though of note: it does see the files.

Is there any other way to access the certificate store in Firefox for Android or retrieve the cert/key db files from which I can extract the certificate?