complicated probability question

I've been working on this for a while and I was hoping for some verification that i'm on the right path:

Given a 6 deck shoe, dealer hits soft 17, how many unique dealer hands are possible?

AceSpades-7Diamonds is unique to AceSpade-7Clubs
AceSpades-7Diamonds is NOT unique to 7Diamonds-AceSpades

A few rules I think i've discovered: Suiting will only matter if there are more than one card of the same rank (not same value) in that dealer hand.
In the event two cards are of the same rank, there are 336 combinations and 10 different ways for those two cards to appear (SpSp/SpCl/SpDi/SpHe/ClCl/ClDi/ClHe/DiDi/DiHe/HeHe) == (6*5)+(6*6)+(6*6)+(6*6)+(6*5)+(6*6)+(6*6)+(6*5)+(6*6)+(6*5)

For instance, I only see 2096 2-card (pat) hands:
A/K, A/Q, A/J, A/T, A/9, A/8, A/7 == 4*28 == 112
K/K, K/Q, K/J, K/T, K/9, K/8, K/7 == 336+4*4*6 == 432
Q/Q, Q/J, Q/T, Q/9, Q/8, Q/7 == 336+4*4*5 == 416
J/J, J/T, J/9, J/8, J/7 == 336+4*4*4 == 400
T/T, T/9, T/8, T/7 == 336+4*4*3 == 384
9/9, 9/8 == 336+4*4 == 352

I also can't seem to find an equation to make this simple, since this is sort of combinations and sort of permutations. (order doesn't matter on T-6-5 but does matter on 9-7-A)

Any help would be appreciated. Thanks.

If only rank is considered without regard to suit there are 1,677 possible dealer hands if dealer stands on soft 17 and 1,740 possible hands if dealer hits soft 17. This assumes 3 or more decks. For 1 or 2 decks, there are fewer possible hands.

Do you mean multiple card hands, or just 2 card hands? multiple card hands, this gives me a light at the end of the tunnel.

Dealer wouldn't get a chance to hit or stay on soft 17 if there are only 2 cards involved in the dealer's hand.
I've been dealing with soft 17s in the 3 card, 4 card, 5 card, and slowly working on 6 card hands, and a part of my worry is that i've missed a few combinations of soft 17.. worried i'll miss a bunch of valid dealer hands and hoping there might be a program or list of them.

Unfortunately suit does matter for this.
It doesn't matter how many decks are involved, until identical cards are in play on the dealer hand. ASp(deck1) 7Sp(deck1) is not unique to ASp(deck3) 7Sp(deck3), so there are only 4(number ace suits) * 24 (number of k/q/j/t/9/8/7 suits) unique combinations there.

When the number of decks does matter is when one of those cards has been removed on the previous draw of that hand (or technically a previous hand, but calculating card removal over many hands would make this completely impossible without a computer). So KSp(deck1), Ksp(deck2) is not unique to Ksp(deck4), Ksp(deck2), but the number of combinations for the second KSp to come out is less since that first card's been removed.

To make this simple for my charts (trying to figure this out in XL) I combined all King,King combinations into a lump 336 combinations... but i think that number's off now.
King(Sp) King(Sp) there are 6*5 cards to make that combination. King(Sp) King(Cl) there are 6*6. K(Sp)K(Di) there are 6*6... etc from my previous post.
This 336 idea seems to be another weakpoint though..

Hmm... suit does matter though. Any further advice anyone please?

I think suit only matters if you are considering bonus payouts for certain player/dealer hand combinations where the rules are that the hands must consist of specific suits in order to qualify for the bonus. For typical rules this is not the case.

i.e there is no difference in a dealer hand of ace of spades, 2 of spades, 7 of spades and a hand of ace of diamonds, 2 of clubs, 7 of hearts. Order of the cards does matter, though.

I think what you're trying to do is to compute the probabilities considering all of the cards sepearately. This can certainly be done but it is simpler to group cards by rank. i.e. in a 6 card deck there are 96 tens rather than 6 tens of clubs, 6 tens of diamonds, etc.