You can always try to assign a particular type of instrument in an ideal tuning, but the term "lute", in any language form, is a generic term for a "family-context" of instruments. Unfortunately with Vivaldi, the fact that it may be difficult to play or go "off the range" is absolutely not relevant, as is the case in his other concertos. Remember this is the guy who writes the violin parts in bass clef sometimes, which you would need a reverse capo for. Not to mention the recorder concertos, and so on.
Even octave doublings, alas, do not give us a real clue, but the mandolin fits the range nicely, and so do other lutes. Some people play it C major. As for mutes, looking at Juditha Triumphans, we see, as elsewhere in the canon, that V. calls for lead mutes for his mandolin aria. These lead mutes are perfect for example the slow mvt, and if covered with leather are safe to use. Some scholars venture that mutes were not used on the cello in the baroque period, but that of course is not true; however, they may have been less common, especially if using all gut strings for the cello. So you can play it on any lute, and if you wish to be in the same octave, you can play it on a smaller lute, and if you want it in meantone, the mandolin tuning, with the high G ( or even E, but the G seems better to me), works perfect with no tastini which are a chore on the mandolin. MT works because you have open B and E in the middle courses, and if you tune your archlute 4th and 5th courses down a half step that works very nicely as well, also for the modulating bit. Remember also that V did not write violone parts for 99 percent of his works, and in the extremely rare place where the violone pops up, it may be a cello or "church bass." And, lastly, one of the many, many meanings for "concerto" is "quartet," so it is fine to play it as a quartet of two violins, lute and BC. dt To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html
