You are on the right track but it's just that no one has given you the break. Most MTs start with clinic notes and then wait for a break into the Big 4 doing acute care. Don't get discouraged. Yes by all means, test away and you might just get lucky. Take any job you can doing acute care even if the pay and hours are bad just to get experience under your belt.
It's not easy making a go of it these days even with tons of experience. Ya gotta be a little clever and have a game plan. Look at it as a challenge and keep at it. Best of luck to you.