The PCI DSS isn't expressly clear on this topic. The meaning of secure key storage and secure key management is left up to the QSA's interpretation. You may find that that one QSA considers the private KEKKEK* to be all that needs to be secured, and he treats the EKsEKs* as tokens. Or you may find a different QSA that sees every individual EK as needing to be secured, even though they've been encrypted with a KEK. We've had both kinds of auditors, and frankly, I thought the "harsher" of the two was more competent (even though I disagreed with his assessment of the risks.)
The bigger problem I see is that you're not taking into account the cost of owning this system. A complex system like this is going to take time and money to build. It will require the auditors to make a very careful examination of all the nooks and crannies of the systems, which will also take a lot of time and money. And they'll have to repeat their examination every year.
Consider that under the current rules, if you build a system that gets breached, the rental guy will be liable for 100% of the costs of all fraud associated with the breach. That means if someone steals a millionaire's card and charges a Ferrari on it, he's liable for the loss. If someone steals 10 millionaires' cards and charges one Ferrari on each of them, he's liable for the whole loss. His lawyers, of course, will immediately turn around and sue you for building an insecure system. And they will sue the QSA for incompetence at not telling them that your homemade system was insecure. So the QSA has to charge enough not only to pay for the time spent auditing the system, but also some insurance to cover their risk.
Frankly, the rental guy would be better off having his counter employees making photocopies of customer ID cards and dropping the copies into a drop-box type safe under the counter; and keeping his security cameras rolling. If a customer fails to return an item, or returns a damaged item and contests it, he'll have the evidence he needs to bring the renter into small claims court. That's a whole lot cheaper than building a PCI DSS compliant system and maintaining it. (And that's really the point of the PCI DSS - the auditor should identify and explain the risks, the business owner should carefully consider the risks, and then make wise choices.)
EDIT * KEK - Key Encrypting Key; a “master” key that encrypts all your other keys. * EK - Encrypting Key; a key used to encrypt one or more sensitive pieces of data. Depending on the design decisions, you may choose to encrypt each card number separately with its own unique key. In that case you’d likely have a KEK to encrypt and decrypt those keys as needed. Often the KEK will need to be kept in a Hardware Security Module (HSM) for increased security.