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Bumping the fee rate would cause the transaction to get mined

Only when mempools are not congested. If there is regular traffic with higher fees, then transactions can be relayed for free. By being 100 MB behind the tip, and 4 MB per block, it means at least 25 blocks (and new transactions are constantly created by regular users).

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This is the reason why BIP125 has multiple conditions for a replacement to be accepted:

When you have a chain of transactions, then you have to bump only the first transaction, to invalidate everything behind it. Which means, that you relay Alice -> Bob -> Charlie -> ... -> Zack with minimal fees, and then you bump only Alice -> Bob just a little bit. Guess what: Bob -> Charlie -> ... -> Zack chain is now invalid, because "txid:vout" was changed.

So, you can start with 0.1 sat/vB, then keep bumping Alice -> Bob, until reaching something like 0.99 sat/vB, then start bumping Bob->Charlie incrementally, and so on. Miners using 1 sat/vB will never see that traffic at all, and nodes accepting 0.1 sat/vB will keep broadcasting it between themselves.

Another option is to keep using 0.1 sat/vB all the time, and check, if nodes forget about transactions after two weeks, or maybe faster. And then, it still means free relay of something around 200 MB per two weeks, if not more. Also, when nodes forget about previously broadcasted versions, then you can use exactly the same coins again, to relay different versions of the same transaction, with the same fees, which means, that different nodes will then store different transactions in their mempools (which also means, that you won't pay anything for what was relayed before, unless some miner will allocate some space for low-fee transactions, to stop your attack, and take your coins, while also losing opportunity to get fees from other, more expensive transactions).