Two questions, since for reasons unbeknown to me I suddenly got quite interested in this instrument lately - is yours stringed with gut or nylgut and what you happen to know the wood used for the whole back piece? Also on a more technical level - do you recon it would be possible to have the courses tuned not in unison or octaves but if fourths or fifths?
George Stevens built the instrument and info on his gitterns is here: www.gstevensluthier.co.uk/instruments/gitterns as well as contact info. I have tried with both nylgut and gut and surprisingly could barely hear a difference so I'm back to nylgut for convenience (most of my lutes are in gut and it makes a big difference). I know there are instruments that have parallel fifth tuning (some hammered clavier maybe?) but never seen or heard of it on the lute. If you are just playing a single line I suppose it could work but of course you wouldn't be able to adjust the harmonic interval and some chords and drones could be off. Certainly no iconographic evidence for gitterns to have all the courses with different pairs of string thickness which such a tuning would need
From top to bottom: c, g, d, a, d (octave tuning on the lowest course). For pieces whose mode lives nearer to g, I will tune the 4th course from a to g
There are some similarities although the Mandolin came several centuries later. The gittern can have 4 pairs of strings like a mandolin, they are plucked with a plectrum, and it's usually tuned in 4ths. A modern Mandolin though usually has metal strings
Considering the build there should be no problem at all to install piezo pickups under the bridge, however unlike with guitars you'd have to have the luthier who makes the instrument plan for that from the start.