From my experience loads in J are fairly decent even with 2 flights/day especially in summer months with both business and leisure travelers (plenty of cruise ship traffic). So net is that I don't think they release many J reward seats.

Although may not help you I've seen some reasonable availability in F recently in fact managed to grab 4 F tickets over XMAS/New Year just a few weeks ago which really surprised me since at T-330 I could only find 2.

The other thing to check is that it used to be the mid week flights (Tues/Wed) that were more likely to have premium availability but seems that now the days when 53/49 are operating seems to have more premium inventory available so probably worth it to keep checking and if you find something worth grabbing it straight away.