The best way that I can think of to stay on UA most of the way would have to be PHX-SFO-NRT-SIN-PEN (but that would require an overnight in SIN)with the last segment on SQ. Unless you had miles or system wide upgrades a Y fare won't nessecarily get you into C but it will help you in the priority list. You could also try going thru BKK from NRT but you would still have to overnight.

I think the quickest and easiset way would be to go PHX-LAX-SIN-PEN with the last two segments being on SQ. The LAX-SIN would be on the A345 which is executive economy and business class and from what I hear is fairly comfortable. I think this would make sense as being the quickest and easiest way to get there. This will probably be the best Y service option and quickest with a 25 hour travel time.