In that case I would jump on any J award you find, and hope that another one pops up before you need to purchase.

There is no guaranteed pattern to ticket pricing. It depends on demand of which you have no control. But, I find 6-8 weeks out to be generally a good sweet spot for international ticketing. It might not be the cheapest time to buy tickets, but if demand is low airlines often reduce prices around this time. And prices often go up when you get less than 6 weeks to the departure date.