It is possible to make the client counting the amount of CLAMS digged in the past 24 hours. If it exceeds certain limit then trigger DoS in mempool to reject newer digs, or give the diggers an option to proceed with a significantly higher tx fee.
The significant higher fee is actually an idea i like.
Yes this is also what I prefer. If the diggers insist to proceed then he will need to pay a lot more to existing stakers/holders.