Guitar Patterns Major Third Tuning Part 3

Question

As I was looking for possible string groupings for fingering chord shapes I came across a few unique set of string sets that would allow new types of chords to be played. For this unique set of string combinations I'm looking for the number of possible unique chord fingering combinations I can make. If I learn this set of string combination I would by now figure out all the possibilities of 4 note unique chord shapes of my Guitar (tuned in Major Thirds). So this would be my Last Last question (seriously!). Here is this set of Strings

            . . . .
            . . . .
            . . . .
            . . . .
            . . . .

In this set there is actually 5 strings across the fretboard (4 frets only). Strings are horizontal. Frets are Vertical. We're omitting the middle third string for this analysis. Here are chords that are acceptable

            . X . .              X . . .
            . X . .              . X . .

            X . . .              . . . X
            X . . .              X . . .

The X's are the notes of the Chords.

Here are five rules that must be accounted for.

1) No chords that have notes exclusive in frets 1 & 3 and also frets 2 & 4. They are not counted in this analysis. Here are the examples:

 . . X .                    . X . .
 X . . .                    . X . .

 X . . .                    . . . X
 . . X .                    . . . X

2) No repeated shapes transposed sideways in a different place. Its necessary to have one shape but I don't want see a repeat(s) of that same chord shape counted in the list of possibilities (pretty redundant).

 . X . .             . . X .
 . X . .             . . X .

 X . . .             . X . .
 X . . .             . X . .

   Okay              Not Okay

3) The chord must always have 4 notes.

4) No multiple notes in the same string. (Its not how the instrument works)

5) This last rule is unique. Take a look a these

 X . . .       . . . .        . . . .       . . . X
 . . . .       X . . .        . . X .       X . . .

 X . . .       . . . .        . . . .       . . . X
 . . . .       X . . .        . . X .       . . X .

                                           Not Allowed

The first three charts shows note doubling. Strings 1 and 4, and also strings 2 and 5 cannot have notes on the same fret. an example chord in the far right is shown. Chords with note doubling on strings 1 and 4 & string 2 and 5 in same fret are not allowed in this analyses.

That's pretty much it. If you can find the maximum number of combinations of chord shapes possible taking account of the 5 rules please let me know! I would very much appreciate it

(Links to First Two Parts Added)

Part One - Guitar Pattern Question (Major Thirds Tuning)

Part Two - Major Thirds Tuning Guitar Pattern Question Part 2

P.S This is basically the same as part 2. The only difference is that now there are more instances of note doubling in chords.

EDIT: I think I just found out the answer! Its 104 chord shapes. Lots of counting and second checking for that one.. !