There are so many things wrong with this idea it is hard to know where to start. First, the C bout in the violin waist area is were you instrument is bowed. If you were to position the bridge so you could bow in the waste area of the uke body, the bridge would be sitting inside the hole. That won't work. If you keep the bridge where it is on the uke, you could not bow the strings because of the larger lower bout, the bridge would have to be way to high which is not good. That won't work. A standard 4/4 violin has a scale length of about 13 7/8" so the bridge has to be placed on the uke top where it will do the most good which is the center of the lower bout.
The sound post in a violin it there because the back has to be incorporated into the violin sound. The violin has a bass bar under the bass foot of the bridge. The sound post and bass bar are the only thing supporting the CARVED top plate. The top plate is carved because the string pressure is too great for a flat top instrument.
Using nylon uke strings with a bow is going to sound very sad and flat. Then there is the curve of the fingerboard and bridge, and on and on and on.
Maybe because I know what is involved with a violin and a uke from my building and repairing both instruments, I can see all the problems and pitfalls with this idea. If you should attempt this idea, it will be interesting to see the result.
