Have you done a load demand calculation to see if the added load can still be served by a 200 amp service? (I question this as you said the 200 amp panel is full)
I second that you have a problem with the requirement of the grouping of the service disconnects required in 230.72 which the Midwest meter main would solve if you have the room, which is the same reason you can't use the suggestion that kwired posted in post #6 again because it would violate 230.72 (which would be allowed for a detached building)
I believe that someone also makes a meter main with just a 200 amp and 100 amp, but I couldn't find one when I started a job I'm doing now as in this case I have a dwelling over a small store where I needed a single meter with a 100 amp for the dwelling and a 200 amp for the store, so with the owners blessing (because of the cost of the meter main panel) I opted for two disconnects off the meter base (320)
Photos in post 23 of this thread
Very few 200 amp meter bases have studs for changeable lugs, so finding one to install double lugs can be a challenge although I have installed them I think they were Durham something (Not sure of the spelling) but they are not a common meter in this area since the utility quit supplying meter bases, now Milbank or Midwest is the most common available. Square D has options but they are pricey also.
Not many options if the home owner wont allow you to run back up and out of the 200 amp panel.
And Welcome to the forum:thumbsup: