Sound post or Under-brace ?

So, the 'concept dulcimer' I am building is coming along now, and I have a question...

As you can see by the attached photo (hopefully), the fret-board doesn't extend the length of the top, so there will be need for support under the bridge (the dulcimer top is 3/16" maple, the rest is 1/8" cherry).

One thought is to install a Sound Post inside the body (under the tenor side of the bridge, giving support from the bottom plate).

Another thought is to glue a solid brace inside the top plate (beneath where the lower fret-board would have been).

The aim is to keep the top from collapsing from the tension from the strings on the floating bridge.

Your suggestions would be greatly appreciated!