Finding transpacific award flights in J/F hasn't been that difficult for me.
Currently I have award trips for next year booked to Fiji & Australia (Fiji Air and Qantas), and Japan & Tahiti (JL and Air Tahiti Nu). All flights were found/booked with less than a handful of 'search sessions'. All J or F.
The key I think is having at least some amount of flexibility. You have to be willing to a) grab an available award that is reasonably around the time frame you want to visit, and then tailor your dates & trip around the award flights, and b) be willing to take a positioning flight if necessary, one that you may end up having to pay for.
If you have little or no flexibility, i.e., you're looking to travel LAX - Sydney and back on two specific dates in January, in F on the A380 on Qantas, yes -- it might be years, if ever, before you find an award. Add maybe more years if a same ticket award seat up front on a connecting flight to LAX is a deal-breaker.