Did a similar thing about 25 yrs. ago...had 12 cars, small apt...house hunting all the time. I mostly used the 32ft. units, and kept 2 cars in them, but, had a few singles that were 20ft. long. Climate control was not an option. About once a month, I would gather up my Wife and bro-in-law and transfer all the cars to the apt...work on them, and then drive them back...taking care NOT to be observed while placing car in a specific unit (and, if observed, moving it later to a spare unit, which would leave a would-be-thief with an empty). Another friend had 20 cars at same location...neither of us had any problems. Was VERY RELIEVED to get into house, and bring most under one roof(Porsches and Jags are MUCH smaller than Vipers are !!!).
Is the 15ft. length an INSIDE measurment?...I found the lengths to be overstated, causing me to move to 20ft.
The ILL. Club is a great bunch...you just MIGHT pick up an offer to store it for you as others read this post.
Good luck.