If it’s easy for the attacker to send transactions to almost all miners without you seeing them, then they can publish state K, then broadcast state K+1, K+2, K+3 at each new block height at a higher feerate than your proposed update to state N. If you saw their tx prior to it being mined, you could just update your state N tx to spend K+i+1 instead of K+i, but only if you see their tx. Blocking you from seeing their txs in the mempool is probably not too difficult if they can directly connect to your bitcoin node.
Hard to do if you have a working watchtower arrangement, even one that’s merely independently watching the mempool and sending you unconfirmed txs it thinks you might be interested in.