The real answer is to increase the layer 1 block size, so it's useable. While that is outside the scope of what you and me control, we do have the power to culturally infulence those around us to make that happen.

But this of course not what you want to hear, so,

Really transfers both on layer 1 and 2 are messages that are signed. With the layer 2 being an IOU. If you don't onion route it through the current system, I don't see why it can't be sent like a regular message. Right now I'm sending you this via Nostr and signing it. You can read this when you're online, but I don't have to stay online for you to read it. So why can't I send you layer 2 messages, and a server stores the message, but not the private key? It's all a game of who has what data when. There could be ways of having the reciever keep the private key, and bring it all at once to the server.