Don't use Phoenix then. If I have $50 of Bitcoin on the Lightning network. I don't care about custody. If I put $1000 of Bitcoin on the Lightning network, I'll make sure I have my own keys. "Bitcoin e-cash" is a misnomer. It's not Bitcoin. It's some shitcoin that may or may not be backed by Bitcoin.

I would imagine the relay operates the mint and since lightning is used to get in/out your client could just use lightning to buy the exact amount of ecash needed for a stamp and then use that? Probably still prohibitively expensive with lightning fees for one stamp but maybe you could just round up to whatever makes sense whenever your balance is too low.