Status: conflicted with a transaction with 408420 confirmations
Transaction fee: -0.00100000 BTC
Do these coins still exist somewhere in my wallet?
Is there a way of recovering them using wallet surgery or another method?
no, they don't exist in your wallet anymore, you have used them in another transaction
easy way to figure this out is to check the balance of sender address on a public block explorer
if there is an utxo shown (balance discrepancy) on the explorer but not on your wallet, then you can recover it
and to fix/clear those conflict notifications, follow NeuroticFish suggestion,
zapwallettxes should do the job