Any Sonic Benefit Tri-Wire vs Bi-Wire vs Single ?

Yes, it really depends on the speakers.
My currrent speakers benefit greatly being bi-wired.

Since your speakers manufacturer went to the trouble of setting up yours in tri-wired configuration, it probably would be an improvemnet to bi or tri-wire.
If it was me , I would use thin pure silver on the tweeter.

I don't know that there is any one answer. I've had tri, bi and single wired speakers, tried all sorts of runs, results have been so variable. Ask the speaker manufacturer what they recommend.

In my experience, bi-wired will give you a slightly better sound. To get additional performance from you speakers, you need to go bi-amp.

What speakers are they? If they are Harbeth's you should use a single wire connection and the stock jumpers.