Well that's very subjective. I personally will pick SQ, but once in a while I will go for LH.

PVG – NRT: NH922 - July 1st - 10:15 - 13:55
NRT - SIN: SQ997 - July 3rd - 11:30 - 18:00
SIN – BKK: SQ64 - July 3rd - 13:05 - 14:30
BKK – SIN: SQ67 - July 5th-- 16:10 - 19:35
SIN – LHR: SQ320 - July 6th - 12:40 - 18:45
LHR – FRA: LH4725 - July 10th - 09:45 - 12:15
FRA – FCO: LH3848 - Aug 6th - 16:40 - 18:25
FCO – FRA: LH3845 - Aug 12th - 15:00 - 17:00
FRA – JFK: SQ26 - Aug 12th - 08:20 - 11:00
JFK – LAX: UA25 - Aug 18th - 11:25 - 14:28
LAX – SBA: UA6155 - Aug 20th - 17:04 - 17:44
SBA – SFO: UA6377 - Aug 21st - 11:57 - 13:15
SFO – SEA: UA970 - Aug 22nd - 12:50 - 14:49
SEA – YVR: AC8094 - Aug 24th - 12:55 - 13:47
YVR – LAX: AC552 - Aug 26th - 08:00 - 10:48
LAX – NRT: NH5 - Aug 27th - 11:35 - 16:20
NRT – SIN: SQ11 - Aug 28th - 19:00 - 01:30
SIN – ICN: SQ882 - Aug 29th - 23:45 - 06:55
ICN - PVG: OZ365 - Aug 31st - 14:10 - 15:00

Sorry for the big wall of text, but how does that look?

It doesn't look very healthy.

You have negative connection times in SIN the first and third times you visit, and in FRA the second time.

And you've got two >24hr stopovers in LAX.

And what are you going to do in FRA all that time, when the stopovers in other places are so short??

Try plugging it into the *A rtw mileage calculator.

I got the dates for FRA messed up. I don't see a problem with the third time at SIN.

"Two >24hr stopovers in LAX" ? Since when?

Erm...

1. JFK � LAX: UA25 - Aug 18th - 11:25 - 14:28
LAX � SBA: UA6155 - Aug 20th - 17:04 - 17:44

and

2. YVR � LAX: AC552 - Aug 26th - 08:00 - 10:48
LAX � NRT: NH5 - Aug 27th - 11:35 - 16:20

Big deal, I'll just take a later flight to LAX from YVR.