Can I apply for a non-B extension of stay before my current one expires, and will it always start on the same date each year?

Even if you go before the 15th, they will still give you a year starting on the 15th, if everything is okay at least. No worries.

Most immigration offices allow you to apply for a new extension when you have 30 days or less left on your current one.

Many Non-B extensions get a 30 day under consideration stamp when you apply and then you go back on THAT date and get the yearly extension inked into your passport.

It won't go under consideration until your current extension expires it goes under consideration for 30 days from the date you apply for the extension THAT's the date the stamp says to return for the "results" <- meaning to get the rest of the year extension inked in.