I'm not a mechanic, but first guess would be that it's fuel-related. Meaning lack of it(pressure) or something else. As far as you "working it" and giving it throttle: Do you try to get it to start w/o even touching the gas pedal the first couple times, or do you quickly start giving it throttle if it doesn't immediately start?

I'd try w/o touching the pedal at first, and if/when that doesn't work, I would do what the manual says to do in cold starts/no-start conditions. Just follow those steps exactly, first you give it partial throttle I think, working your way to full throttle if each previous step doesn't work. If that helps I believe it would point to a fuel issue whether it's the filter (that may be an in-tank filter, not sure) or something else.
I believe it also states to wait at least wait ~15 seconds between attempts, might not be a bad idea to try that as well.

edit: do you ever smell fuel the next day, prior to the no-start? Maybe an injector is sticking and flooding the engine:shrug: If you've never used something that cleans injectors (seafoam/lucas/marvel mystery oil being good choices) that might be a cheap thing to try just in case.

Otherwise next guess would be a sensor (such as crank angle) b/c I don't believe a fuel relay would act up in the way you're describing.