The closer dealer should handle the problem. They all work for Mazda, and they all get compensated equally by Mazda for the warranty work that they perform. So it doesn't matter which dealer you go to for the work, as long as it gets done.
As far as I know, there haven't been any issues regarding warranties or warranty rejections on this forum. Your best bet is to keep a copy of the recommended maintenance schedule in your owner's manual, and keep a log of when you did the service, as well as a copy of the invoice for that service that shows the date and the tech's signature. Alternatively, if you do your own maintenance like change your own oil, change your own cabin filter, etc., keep a log book of when you did the service, the mileage at the time, and keep receipts of the parts you used for the service. Also note when you perform self-inspections and when you lube the joints.
I believe the 1000 miles applies to 1000 miles after 15k or 22k. So if you perform the recommended maintenance at 15,700, then you're all good. But If you perform the 15k service 16,500, you might have issues. I don't think its that big of a deal though, it's more important to show that you performed the recommended service (or had the service done for you).
Thank you Sm1ke for your reply!