I've two observations. The first is that I don't have a good understanding of your threat model. Either you have not explained it very well or I'm being dim. I understand that you are attempting to protect a collection of 10-digit numbers but I do not understand the nature of the attackers against whom you are attempting to protect your information. Without a good threat model, evaluating security is almost meaningless.
The second is that this scenario seems to cry out for public key crypto. Issue all your data collection laptps with a RSA public key. Extend the data with a random sequence of digits so that exhaustive search with work function of 1e10 can't decrypt the data. Keep the private key secret. Anyone who can break kilobit RSA undoubtedly has the capability to break your security by other, cheaper, means.
Paul
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