There is a lot that is unknown. I would think it is odd to have both the 125/240 and the 120v 30 amp connected to a breaker panel. You either have the 125/240 or the 120v 30 amp connected to the breaker panel, not both. If both are connected, and if you have the 125/240 providing
power, then the 30 amp connector will have voltage on it. Someone opens the cover and touches the exposed terminals, and they will be shocked.
You need to figure out which is really connected to the breaker panel. Ultimately, the solution could be as simple as you suggest, ie add a 220 volt outlet and circuit breakers. But it could be more complex.