Well, this isnt at all a simple problem. The manual way which takes considerably less time than a hour, which would also have done the first step for free, is as follows:
Open in inkscape or illustrator
For each area:
select text and polygon, and group it (hit ctrl+g; same in all apps)
Text and polygon is not next to eachother in a shared group.
Here's one possibility with Inkscape
In the example below, I did a Trace Bitmap in Inkscape, using the "invert" option.
Then I selected the drawing, and set the fill to white (this will make it disappear temporarily)
Then I added a thick black outer stroke, with rounded joins
With the Bézier tool, I redrew some of the black areas that are ...