Regarding material length, if i am designing something 12" long then i leave myself at least 1" at the top and bottom and set your start point at that 1" from your chuck so as to preclude any bit hitting anything.
Once you do that you will always have enough material to hold your stock. You might want to post a picture of what you are trying to make so i can better understand what you are doing.
Your design should NOT go all the way to centerline, without adequate support it will just break.
On most carving designs your depth of cut is usually the same as if you were carving something flat on your table. The only time you will cut way below the surface is if you are making something like tenons on the ends of your material like for balusters.
You would then want to look into some type of "thin stock support" and when you need advice i have a nifty gadget you can use ( a kids skate). see pic
Do you just go modify your designs so that they are short by 1/4", and you wind up cutting off a 1/2" thick (if it is milled 1/4" short on both sides of the centerline, it SHOULD leave a 1/2" thick stub, right?) And: Is that enough in a slow turn situation with little material being taken off?)
Now ask yourself, if i'm not making this (.5" stub) part of the design of the part, like a tenon, then why cut it down to .5" in the fist place? Just take your part over and cut your ends off at the bandsaw or tablesaw but leave them big and you have no concerns about breakage.
The problem you have is both downward pressure from the bit and lateral pressure from the tailstock pushing the material to hold it tight will allow it to break.
What if I can't get that onto the bed of the machine? What is my stock is blocking that?
The wooden jig that i made is the height from the bed of the aluminum plate to the centerline of the shaft on my indexer. I can usually turn the jig longwise (in the X) even with 3"-4" stock in the chuck and still get a Zzero.
If not then move your indexer down the aluminum rail to give yourself about an 1 to 1.5" behind the back of the indexer and you can use that space to Z to even with material chucked up (I forget to Zzero many times till AFTER i have material in chuck).
The drawback is you lose that 1.5" in length of stock you can use in your Y direction.
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