IIRC nodes only store up to 25 transactions in an unconfirmed transaction chain in their mempools. Anything more than that will not be kept in the mempool and will simply be rejected.
You are right. 25tx or 100Kb.
So considering that maxmempool default is 300MB, and maximum chain size is 100kb, you'd need 3000 chains to clog the mempool.
To bump the minimum fee from 1000 satoshi/kb to 10000 satoshi/kb would only cost 0.3BTC
Also, I think since changing that transaction would invalidate the entire chain, the chain would also be discarded.
Yes - the chain is discarded but I don't think the minimum fee is updated when this happens.