There are a couple of good looking electric ouds made by Viken Najarian
Review of the E-1000 on Harmony
There`s a clip on this site of one similar looking to the Najarian oud. Noisy and cheap
sound quality but gives an idea. Site seems to be inactive.
Lark in The Morning has an electric oud by "Renowned Turkish luthier Saadettin Sandi"
other places to look
The message board on unfretted can probably answer if fretless guitars like the Godin Glissentar
may sound oudlike with some EQing.