When is the earliest I can apply for a new Non-O retirement visa before my current one expires?

As a general rule you can apply for a new year extension when you have 30 days or less left on your current stamp (Some offices are 45 days but figure 30 or less and you're always good)

So in your case, any time after June 18th

Most immigration offices accept the year extension application when you have 30 days or less with your current stamp. I think Samui, too. But let's see if someone knows. Or try to post on Samui related groups you may get the answer quicker.