"...it won't match up with adjacent rooms (living room, family room and dining room. I don't really want to replace all the woodwork at this time. Any suggestions?"

Is the molding continua a round walls into other rooms?

If there is any break no one will notice the height change.

It is is continuous this might be the time to add molding around the openings into other rooms (often called casing).

It goes around corners leading into the other rooms, but there are no doors to break it up.

Remove the baseboard and then place it on top after. You can do what is called 'return ends' where both baseboards meet. It may require you find small pieces to make the return ends. Return ends work well to make mismatched heights look normal.