just signing the transaction via the relay provider but use a custom provider to relay it
Even if you did that, the tx would be invalid in the other chain due to EIP155 replay protection. Now, I understand that this is required for bridging from Ethereum to Polygon (I got a message from Peter on this). Let us see if there’s anything we can do about it.
Update: I’m going through Polygon’s docs, and it’d seem that it’s possible to deposit for a different address when bridging assets. The bridge contract exposes a
depositEtherForUser method that accepts the address on the other side of the bridge, which seems like it can be different than the sender. Can you confirm this?