i dont think the p0300 code was from this, like i said last night that is a old code that isnt related. your tranny acting up WILL NOT throw codes. and AWilson also said that that code needs to be accompanied by another code like p0301 or 02 ect to indicated which cylinder is misfiring. i think that code was never cleared and when the guy pulled the codes he pulled an old code that is not related at all.
i would take it to an independent shop that is a full service for asian vehicles, and have them take a look at it too. a tranny shop will tell you its the tranny or tq converter most likly cause thats what they do and they want to sell you the work. get more than one persons(shops) imput here. if multiple shops start telling you the same thing, boom you have your answer. i still think its the tranny just cause of the mileage of the vehicle and your description of the problem. but with out driving it its hard to be sure.