I just called in to book our trip after the online tool gave me an error, and got a great agent who said that as of next month they will no longer be able to force these longer connections as the partners have been complaining.
I managed to book
YYZ- LAX AC J
LAX-TPE Eva J
TPE - DPS Eva J- destination
DPS-SIN SQ J (20 hr layover)
SIN-MLE - SQ J -stop
MLE - IST TK Y (EF flight alert set for J) 8 hr layover
IST-LHR TK J
LHR - YYZ AC J
Total for 2of us $525.12