The only thing I could think of is the transposition trick.  Do one section as is, do another section half-step down with pitch shift, and then one section half-step up with pitch shift.  

The main way to do this is use two instances of the full sections with pitch shift down/transposition up (not the reverse) equally on all players of one full section.  If you do it for all of them, you will maintain the "Dimension"  interaction of the players properly within each group and double the size.   Also as pointed out it is essential to use different humanize settings for both delay and tuning for each player.  Keep in mind that with strings, it sounds natural to use a lot of humanizing.  I was just noticing the other day that humanize in tuning which sounded horribly out of tune in a woodwind section sounded perfect in strings.  It has to do with just how much lack of perfection there naturally is in even great string ensembles, far more than one might imagine.  

Do the "force G string", "force D string", "force A string", and "force E string" share any samples with one another? If each set is completely independently sampled, then they could be used together without phasing. Perhaps one solution would be to have a 1st Violin section comprising the "regular" samples and "force G string" samples, and a 2nd Violin section comprising the "force A string" and "force E string" samples.Of course, if the sets share samples, then phasing would preclude this solution. Has anyone tried this?

So do you mean:

Violins 1 = 12 players

Violins 2 = 12 players

If yes, I probably would not approach it this way. Dimension Violins has 8 players. I would mimic the LASS approach and simply use a second group of 8 to create Violins 1 = 16 players. I've done this and have not had phasing.

Then, using William's approach, I'd use the transposition trick to create Violins 2. Then I would mimic the LASS approach and use a second group of 8 to create Violins 2 = 16 players.

With this approach you now have div a 2 of 8 players in Violins 1 and 8 players in Violins 2.

If you want more than that, you can now do div a 4 with 4 players each in Violins 1 and 4 players each in Violins 2.

With this approach you can now approach the scoring techniques of Wagner, Bruckner, Mahler, Vaughn Williams and others, that previously could not be executed with any other library.

lol wait for the violas!! haha

John, that also depends on your definition of a "full string section".  DS only comes with half the instruments you've listed.  You'll find that only huge Romantic writing requires nearly that many string players.  That style of writing, however, would not require each of the sixteen first violinists to play separate lines!  So either way you'll need a lot less instances than that.

 I think you're still not clear on how to set up a standard template. Some people, myself included, would use VEP5 to do that since it helps manage various things and also plug MIR into the end result, so let me speak in those terms (sorry if this adds another bit for you to consider, that is VEP).

On one single instance of VEP as your host, add 8 VIP instances, and add each one of the individual DS violins to each VIP. So VIP1 will play DS Vl1, VIP2 will play DS Vl2, etc. So you have 8 individual players for you to write for as you wish, each routed to a separate MIDI channel. Now, on your DAW or notation software you replicate the setup, and have 8 separate staff parts. Unison play? You write once and copy+paste to all parts. You want Div2, write the two different lines on Vl 1 and 5, copy/paste 1 to 2,3,4 and 2 to 6,7,8. And so forth if you wanted other divisi configurations. So that takes care of your first 8 violins. Hope that's clear.

This is not extremely CPU or disk intensive, but it does take much more computer power than most other libraries, as in the end, DS is comprised of a set of individual instruments, just as if you had 8 instances of the Solo Violin playing simultaneously. But I don't want to digress much.

Now for your second group of 8 violins, you have a few options. First, what has been mentioned about detuning and transposing another group of individual violins just as above. Second, could be for you to utilize the desks or 4-player presets included in DS by VSL. You could set up the 4 desks and the 2 4-player groups and use different humanization parameters, and use different EQ settings, to make them sound slightly different to the individual violins above. Then on your DAW, you'll include separate staff lines for each desk/choir, separate MIDI channels, and write there whenever you need to.

In the end, the most you'll have is one VEP port, with 16 MIDI channels / 16 VIP instances (or less if you use the pre-mixed desks), for all your complete 16-players violin section. Then do the same for the Cellos, etc.

This is what I do, and I didn't win the lottery... yet.

Hope this helps.