One thing to keep in mind, though, is that these layers on top of Bitcoin (Counterparty, Omni, coloured coins and perhaps there are more) "are" not really Bitcoin (they just use Bitcoin's blockchain for consensus). So in that sense, an Omni token would not really be a "Bitcoin" stamp. For a "real" Bitcoin stamp, I think the main / only option is to have essentially funded paper wallets as you described initially; that would be quite boring in comparison, though.
I think that still would be fine.
The original crypto stamp isn't an
etherum stamp either, but an ERC-721 token.
Using something like bitcoin / omnilayer should be comparable to ethereum / ERC-token. Or am i missing something ?
I am not really familiar with omni, but as far as i know thats pretty similar ?