Upvote:1
Croatia would be your best bet by car if you really have to leave the Schengen area. Though it is quite out of your way.
Were the authorities aware of the other visa when you made this plan? As it seems a remarkable coincidence that one begins just as the other starts if so. I'd guess that they're valid; One expires at 23:59:99 and the other begins at 00:00:00 so there's no time you're actually outside of a visa.
At absolute worst I don't think such a minor oddity is going to get you in trouble. Though of course best to check with the authorities.
Upvote:2
You do not need to leave the Schengen zone in order to transition between back-to-back C visas. Issuing visas back-to-back is the normal, expected way to "extend" the validity of a multiple-entry visa. You just need to follow the 90-of-every-180-days rule at any time -- the new visa does not give you a "fresh account" for that.