I am pretty proficient with my straight, now. Was where your at about 8 months ago. I am far from being an expert, but I would really suspect your edge is lacking. When one of my razors needs a refresh, I am still getting a pretty decent shave on my cheeks but the chin and neck are what tells me that it is time to refresh the blade. Just learning the state of your edge takes time, I'm still learning and that is one reason I enjoy a straight so much, it ain't easy.
I had no mentor to watch me and it took me about six months to really start doing a good job stropping. I started by hurting my edge, then not getting it any better but not hurting it and finally I was able to start improving my edge by stropping.
Keep trying and practicing and you will start getting great shaves, with just your straight. But as TC said go ahead and finish with your DE while you practice with your straight.
Don't give up, your most satisfying and close shaves are very near.