OK I finally got it.....

YYZ-FRA (LH J)
FRA-SIN (SQ A388 J)
SIN-MEL (SQ J)
MEL-AKL (NZ J)

Here's the fun part.......

AKL-NRT (NZ J)
NRT-EWR (CO J)

I wanted to add YYZ, but

(1) needed a good reason (as to why I changed the route when I get back essentially the same time)......

(2) already exceeded MPM by 700 miles... going back to YYZ would exceed over 1200 miles (because of a reduced rate for MEL-YYZ & extra travelling mileage incurred)

Therefore, I just left it at EWR and decided to walk home