Absolutely, yeah. WebCrypto has support for keypairs that can have the private key data extracted (there are limits, though, which I cannot accurately remember

Absolutely, yeah. WebCrypto has support for keypairs that can have the private key data extracted (there are limits, though, which I cannot accurately remember) from the JavaScript object in which they are contained. So it ought to be possible to extract the key data, encrypt it (also using WebCrypto) and sync it (somehow) to another device.