Pete,
I have limited autoharp experience, but I'll share what I know. The autoharp was first designed to be played on a table. The concept of the autoharp was to construct an instrument where almost anyone could play music with little training and/or skill. The instrument was desinged to be placed on a table with the "long" side nearest the player. The player could press the chord buttons with the left hand and strum the strings with the right, utilizing the string area which is now to the right of the chord bars.
As some folks wanted to make more "complicated" music with this simple instrument, the "close to your chest" method developed. This enabled the right hand to have greater access to a broader string area and to thereby develop more complicated strums. The thumb covers the bass strings and the fingers can cover the middle and high notes.
This is not a comfortable way to hold the instrument, because the instument was not designed originally to be held in this way.
Within folk music, the "chest" method became the preferred method. Newer autoharps were designed to be more "friendly" towards this approach, hence the reduction of string space on the one side that you mention. It gives more string area to those playing the "chest" position, especially opening up more access to the treble strings. Some newer autoharps have been shaped to be more accomodating to holding upright. Some don't even have little feet on the back, making it difficult to play the autoharp on a table because it slides around and tends to rattle from inconstant contact as well.
Hope you find this helpful. If you use the forum search and type in autoharp in the body section, you will find other threads about the autoharp that will lead you to other sites dedicated to the autoharp. They may have more information about these two styles of playing.
Roger in Baltimore