I'd like to discuss the pros/cons of implementing lattice signatures in bitcoin now such that when ECDSA is broken it's an orderly transition to use a different lock on funds.
I have little knowledge about cryptography, but you definitely need to be specific. There are many lattice-based cryptography out there such as "NTRU" and "LEW".
I'd also like to suggest that we add an optional PoW on a transaction submitted to a node so that when someone submits their transaction they can provide a PoW of that Tx alongside to the node to show they really want the tx to be included.
In normal usage like we are today, no PoW for a Tx is required. But if there is a systemic compromise of existing transactions, this PoW feature could be enabled by miners such that they only repeat a tx with PoW offered along side it. This way even if the unlikely event of a large QC being made and used to attack the network happens, there is a plan on how people can safely move their bitcoin to an alternative locking mechanism.
This wouldn't work to prevent QC from stealing people's Bitcoin. Average people would use smartphone or computer CPU to perform PoW, while attacker could just use multiple GPU or even QC itself to break PoW requirement easily.