I have never seen anything like that, very cool.
As for the material, I wouldn't use wood, use something harder and with a lower coefficient of friction eg nut or saddle materials such as corian, bone, brass, or some fret wire etc. I recommend black TUSQ XL
As you need to tune both sides of the 'middle bridge' there will be string movement across it and with the significant break angle minimizing friction and wear will be important. As there's no fretting involved presumably you would retune often to get a variation of intervals and available harmony so material choice is important.
I would try making some that sit on the fingerboard (like in the vid) and some that sit on the sound board, I think the later would give better volume. Be aware the soundboard will withstand much less pressure than the FB so bake the contact area larger to lower the pressure.
As for dimensions, I'd just go off whats in the video and work from there (looks 15-20mm to me) there's no big investment so why not make a few and see what you like best. The taller it is the more pressure will be on the FB/SB which may increase volume for the headstock end and improve overall tone but also risks damaging your guitar.
As for tuning I think it's E A C E G A on the body side and A D F A C D on the neck side.
So with the bridge where it is in the vid. the body side is a 5th higher than the neck side. its a nice Am type tuning, if you adjust two strings you'll get an A major tuning:
EAC#EF#A on the soundhole side and ADF#ABD on the headstock side.
As for other tunings, you're limited to only use notes where the complimentary note on the other side of the bridge is also in the key you want. e.g. you may want to have a B when in Am but you may end up with an F# on the other side which you may not want as it's the major 6 not the minor 6 most commonly found in minor keys.