It's just a fact of life that you have to plug an acoustic guitar in when you go on stage. But please, get a better DI box. The difference will be good for you and your audience.
Let me take a step back. Start at the pickups in your guitar. Better pickups sound more natural. That may be enough. But something like a Fishman AURA will make even marginal pickups sound better.
Back when we first started interviewing bands and having em' play a song (this was when we had the radio stations) I played around with different DI's but settled on good microphones. I still prefer a mic'd acoustic in the studio, but on stage you do what you gotta' do.
Most guitars from the stage sound like your head is touching the body of the guitar. It's not natural. It's just a mess. But so easy to fix.
It's another thing to make you head and shoulders above the rest.