Scordatura is a hot topic on all string instruments. A lot of professional violin family instrument players just will not do it, for instance the Mozart Sinfonia Concertante, which should have the violin in standard tuning and the viola up a semitone, is commonly played from published versions in standard tuning.
I think players are more or less polarized so you are either a standard tuning person or a scordatura fan with little in between. Personally I think it is great, though some lyra viol tunings are so extreme they require restringing the instrument which is going a bit far, so I would make a standard tuning version of these. Once you go down that route people then divide into notes versus tab players. I like French tab, just like on the lute as guitar tab looks like upside down Italian tablature to me and my brain begins to rotate when I read it. Another advantage of French tab is that you can put fingering on it without it interfering with the note specification. I have not looked at any Weiss manuscripts for decades but I seem to remember Weiss used French tab.
The Weiss piece should sound much better in your tuning because of the extra resonance. It looks to me as though it has more resonance in your tuning than on the original baroque lute, is that correct? I would love to try it but I can't read the staff notation or the Milan tab... sorry.
One of the most extreme retunings I know is the Biber Resurrection Sonata on the violin where you not only retune but swop the string channels for the middle two strings over. (You can't do this on a guitar unless it has a very non standard bridge.) This results in you having an instrument which, as it would almost certainly be gut strung, cannot be used for anything else that day as it gets so upset by the experience.
Good luck with the tuning and try some other pieces