It sounds like your situation is very similar to mine. I (Female, 23) am in a V at the moment with my fiance (R, Male 25) that I've been dating for almost four years and my boyfriend (D, Male 23) that I met almost a year ago and have officially been dating since January.
It really isn't easy to balance NRE with a long term relationship at first. Here I am, almost a year after I've met D, and I am just now feeling the NRE start to relax its grip on me. It isn't gone by any means, but that first unstoppable wave of it has finally subsided. R has been a trooper, but he has also struggled over the course of that time because he also worries about being replaced.
Parts of our struggle are very similar to what you have already described. R and I have relaxed into a form of relationship where we do spend a lot of our time doing things next to each other rather than actively being involved with each other. R and I both want to do more things with each other, but our interests, energy levels, and motivation can make that somewhat difficult at times. We like watching television shows together and discussing them, but it often leads to us feeling that we still aren't actively engaged when we do these activities.
D and I are still in a phase where a night together is easily used up just playing and talking with each other. When we are all hanging out together, he will also initiate a lot of cuddling or make sure to sit by me, which leads R to feel like he isn't getting enough cuddle time sometimes.
I guess I don't have too much advice to offer up at the moment, but I felt like this was a perfect topic to post in and that you and I could perhaps share experiences and bounce ideas off of each other as we go. R and I setting up a date night that was just for the two of us has helped a lot. And now that I can finally see straight through my remaining NRE, I'm starting to crave a lot of time with R again. It took a long time though and that can be a rough ride while it happens.
Best of luck in your situation, and hopefully we can be helpful to each other. :-)