I don't think you will make it either unless they are using the aircraft from your LAX-NRT for the NRT-SIN segment.
I see UA890 is now due at 11:23am and UA891 is due out at 12:40pm.
New arrival time at NRT is 4:58pm on 17NOV. I guess they expect decent winds because even though they are leaving 1 hr 26 min late they expect to arrive 58 minutes late.
Either way I too agree that 12:40pm is not realistic. I would think 1:15pm is more like it so that would put you in around 5:30pm or so. Not too likely to make that connection.
I see NH5 LAX-NRT is sold out in all classes.
Are you at the airport? There are business class seats on KE2, a 777, at 10:30am to NRT at 3:10pm on Nov 17.
NW1 at 11am also had 8 J seats left. It is a 747-400.
AA169 has 1 J but plenty of F on their 777 at 1140am in on Nov 17 at 4:40pm.
At least that would give you a better chance to make UA891 especially if they had some type of special service meet you at the gate.
On 17 Nov here are some later NRT-SIN flights with business availability:
NW5 has 5 seats 545pm-1230am
JL711 has 4 seats 550pm-1230am
SQ11 has 1 F seat but no business at 7pm
Good luck...and let us know how it turns out!