I am trying to buy a multi-stop itinerary from BOM-SIN-NRT-LAX-SEA-SIN-BOM

I want my NRT-LAX and LAX-SEA legs to be on the same date (given that the flight goes over the date line, you gain a day)
However singaporeair.com does not allow me to book the legs on the same day, it forces me to select the next day for the LAX-SEA leg. And worse does not give me all the options and forces me to select the morning 6 AM flight. Note that the LAX-SEA leg is on Alaska, SG has a code share with AS.

Any way around this, with the limitations on the website?

p.s. I can book NRT-SEA instead of NRT-LAX-SEA and get the flights I want, but this gives me a significantly higher fare, even though the routing is the same.