Although I am not 100% familiar with the product rules, a variation on a theme might be to use an LGLOB39 if you decide you need more flexibility in terms of routing or stopovers:
LHR-DEL-HKG//PEK-HKG-BKK-SYD-PPT-IPC-SCL-EZE-LIM-JFK-WAS-JFK-MAD-TLV//ATH-LHR
comes out at 38,288 miles, although I imagine you would pay a reasonably significant premium over an LONE4 for that flexibility.