Seems you are going to try this come Hell or High Water. It's only money----unless you are out in the Boonies and fry your Li battery bank. Now what?
As long as you have the money to play around with this, and a back -up battery bank, go for it! :)
IMO (which doesn't count), if you are watching a DVD movie, it won't make the movie any better if the inverter is powered by Li or Wets or AGMs. If the movie is the same experience, why mess around with the battery bank if the way you do it now works? Never mind. :)
I think I just said, "Don't fix it if it ain't broke."