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Have you looked into the engine's top end?
It would be good to verify that everything is as it should be in the valvetrain area. Do you have any history on whether or not the valves have every been adjusted? If the valves have never been checked/adjusted that might be (at least part of) your problem.
And I'm not just talking about a valve being a little too tight or a little too loose...
Because... it's also possible that somebody got in there and did a really lousy job of adjusting the valves and really screwed something up. Yes, in cases like your newly purchased bike (low miles bike that sat for a long time) there's often a maintenance related reason why the previous owner let the bike sit for so long. If the bike just doesn't run well enough (and the reason why is unknown) to be enjoyable it will often end up pushed to the back of the garage and ignored.
There could even be a broken valve rocker arm or a missing (lying loose inside the head) rocker arm on one of the right-hand cylinder's valves as a result of an incorrectly executed valve adjustment. In case you don't already now it, the EX250's valve actuation rocker arms will sometimes crack in half (if accidentally adjusted too tight) or will sometimes fall out from under the camshaft lobe (if accidentally adjusted too loose).
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