The tricky thing is that for something more serious to work, you both have to be excited at the idea of trying it out. And right now it sounds like he isn't. So if he's made it clear he's not comfortable with those other modes of communication right now, the kindest option for both of you is to stop pushing for them, at least for now.
That being said, there are still some things you can do to help you both figure out where this relationship is headed.
For instance, have the two of you talked at all about what you're each hoping for from the relationship? If so, how have those conversations gone? And while I think taking the pressure off in terms of calling or FaceTime is sound, if it's more a situation where he really does want to do those things but is a little nervous, have the two of you talked at all about what would help him feel more at ease?