How about this to see if it's worth spending any further time on CLAMs:
1. Sync the CLAM client on an internet connected computer which doesn't contain your private keys. This can be done within a VM, or a fresh OS install, or even a remote VPS.
2. Copy, via sneakernet, the client executable and blockchain data to a NON internet connected computer. Start client. Import wallet.dat, or individual private keys.
3. If balance is zero, stop here.
I was being a little facetious here, but after further thought, I believe you could actually dig your CLAMs. Create a raw transaction (on your air gapped, non internet computer) which sends your 'dug' CLAMs to a new address, then you transmit the transaction (which contains only public info that's going to go into the blockchain) on an internet connected machine.