I think the issue here isn't song choice. The idea that unaccompanied songs going over better than songs with instrumentation behind them ,leads me to wonder if it's the audience (you might just be laying for people who like sea chanteys) or if there is a problem with the instrumentation.
Playing and singing isn't easy. I tend to say otherwise when I'm working with students (if you don't tell them it's impossible they won't try to make any excuses, they'll just do it), but the reality here is that something as simple as keeping a steady rhythm while singing can be a difficult skill to master. If something is off - even something minor - it can hit the audience like chewing on tinfoil. The other thing that drives audiences crazy is playing the same rhythm for a few songs in a row.
My advice would be to do two things. First, just kick back for an afternoon and scope out your chops. I'm not talking anything major here. Just go over what you are doing and look at it from a couple of different angles. While you are doing that start singing every song you come across.
Here's the deal, a song is just a song. If you start looking for meaning in every tune you play you'll wind up as flaky as grandmas homemade biscuits. The "meaning" of the song you are playing is put in while you're singing it. If you're happy, sad, gassy, confused, angry or stoned out of your gonads it'll come across in the song. Going into a tune thinking that you want to say this or that always works against you. Make the song reflect who, where and what you are in this moment in time. That gives the audience a feeling of connection to you, and that leads to feeling a connection with the song.
In other words, don't think. Just sing.