On one of our trips, (Honolulu, I think) there was a business which had vans that would meet you at the airport outside baggage claim and store your luggage in the van. Then when you were finished sightseeing, you called the driver to arrange a meeting place at the airport to pick up your bags and head back into the airport for departure. I was a little leery of this arrangement, but several Trip Advisor folks had used it and gave it a thumbs up, so we tried it and it worked great. I've often wondered if something like that would work at DIA.
The "rent the cheapest car possible and just leave your luggage in the trunk" is an interesting idea. Admittedly, I have not tried this, but if you are a premium hotel's frequent stay program (gold, platinum, or whatever their levels are these days) you might try leaving your luggage with the bellman at a nicer hotel. They generally will hold it if you arrive prior to your check-in time or you're hanging around after your check-out time ... but if you asked (and added a big tip) they might hold your luggage even if you're not staying there.
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Locking options: various types of key locking or padlocking facility are available now. Key locking options include flush locks, cam locks, or locks incorporated into a rotating handle; padlocking facilities may be a simple hasp and staple, or else a padlocking hole may be included in a handle, often called a latchlock. More modern designs include keyless operation, either by coin deposit (which may or may not be returned when use of the locker terminates), or by using electronic keypads to enter passwords for later reopening the locker. Some older lockers used a drop-latch which was incorporated into the door handle, and slid up and down and could be padlocked at the bottom in the "down" position, but these are less used now. Three-point locking is not possible with this type of latch, because it needs to be operated by means of a latch that rotates rather than slides up and down; so this drop-latch is probably a less secure locking option, which may be why it is little used nowadays. Prefect Combination locks are very popular in school lockers used in the UK due to their ease of use and the time and cost saved in the removal of locker keys.