Well, I faced teh same problem with singing along with playing, and what worked for me is not breaking up process in two, but instead integrating singing and playing into one solid process.

What I mean is, for example, you strum a chord and start singing your first note, then sing some more, while that chord is ringing, then simultaneously switch to the next chord and sing the next note along with it. It should feel not like you are doing two different things at a time, but like you play a single melody using your guitar and voice. The simplest analogy is the guitar playing itself: you always use both your hands, though not every note requires a simultaneous movement of both hands.

I don't know if this is gonna be helpful for you particularly, but this is how it works for me.