I was unaware that lutes had an H -string. I want one for my guitar.
As far as DAGDAD goes, perhaps the easiest way to realise how absurd the suggestion seems is to visualize that in order for the tuning to have any sonic integrity you would have to restring the guitar using your third (G) string in place of your fourth (D) string, and vice versa. How strange is that going to feel ? You would need to have a guitar permanently strung like this, so there had better be some really good sounds available.
I think what I find really bizarre is the concept of having the third open string sounding a whole tone below the fourth string. I don't personally know any open tunings in which this procedure is adopted and I find it very difficult to envisage what the unique advantage would be.
I have no doubt somebody will write in and say that David Wilcox or one of the Wyndham Hill mob use just some such weird tuning on some obscure piece .............