I generally thread in the headstock and chamber in the steady. The potion of the barrel which will run in the steady is also turned with the barrel in the headstock.
The only real reason for chambering in the steady is that on my lathe the tailstock sits about .002 high in relation to the spindle center. This unless the lathe has been run long enough to warm the headstock up well. This is common on most lathes and is deliberate on the part of the manufacturer. On a big CNC lathe I ran for a time (28 inch swing)the differential was close to .005 when cool.
Anyway, by using the steady I can be fairly certain the barrel and the tailstock are at the same level and there is less chance of cutting oversize.
The system used by Mike Bryant, for instance, does not center the reamer and it is allowed to find it's own center. His system works very well especially for a barrel which is less than straight and allows him to chamber in the headstock and still be sure of cutting as small as the reamer will allow. The only drawback is that the reamer must be diven (held)by the hand of the operator. This will, with some reamers, be an invitation to chatter. For this reason I like to be able to center the reamer and using the steady allows me to do this and still be reasonably assured of cutting to minimum dimensions.
The reason I thread in the headstock is this; The only sure way of have a true center in the barrel is to dial the barrel in and bore the center. Even a piloted center reamer may cut as much as .0005" off. The point is, once the barrel is all dialed in you might just as well cut the threads at this time as well since they will not get any better by cutting between centers. Regards, Bill.

Clark,
The loose reamer pusher as used by Bryant will indeed work well with the barrel held in the headstock. In fact, it's purpose in life is to allow alignment of the reamer irrespective of misalignment in the tailstock and, of couse to allow the rear of the reamer to float so the reamer can truly follow a misaligned bore. This is all very fine and I have no quarrel with it but I have stated my preference for supporting the reamer on a center to allow for a more solid drive. If the bore is too crooked to allow this, I too will use the loose reamer pusher. In truth I thread and chamber using most techniques at one time or another and find I can do a decent job in many different ways.
As far as removing the job from the chuck goes, I have always figured that if I can set it up straight once, I can do it twice! I have stated my reason for preferring to chamber in the steady ( possible misalignment of the tailstock in relation to the spindle) given my preference for supporting the reamer with a center or centering holder. When I'm about 3/4 through the chamber I'll check it with a dial and, if it is at all out of round due to angular runout of the bore, I'll switch in midstream as it were and use the loose pusher.
Rechambering is often a whole different ballgame since the original threads and chamber are very likely to be eccentric. In this case it is simply much easier to set up in the 4 jaw and do all the work in the headstock dialing in the original chamber. If the chamber is badly misaligned in relation to the bore, I'll dial in the bore just ahead of the throat and take a light cut with a boring bar to straighten things out a bit before rechambering. This applies to a rechamber from a standard to a magnum cartridge where there is a significant amount of material to be removed of course. Obviously, if the chamber is eccentric to the bore, it is necessary to set back by the length of the neck and throat to try and recut this true.
As I said, the loose pusher will work very well with the barrel in the headstock and this may well be one of the better ways to do things in the end.
Other techniques feature such things as mounting the barrel in a fixture much like Tannel's action truing tube and dialing in a rod to ensure the chamber portion is aligned as perfectly as possible then threading and chambering in this. This fixture may be a short one held soley in the chuck or a long one held in the chuck and steady.
There is, of course a drawback to setting up this way to thread. If the bore is too crooked, aligning the chamber portion of the barrel may well result in the rest of the barrel pointing off in a quite unintended direction. In a case like this it would pay to thread between centers or in the four jaw with a spider at the rear to achieve "average alignment". One could then set up with the chamber portion straight to chamber. This way, the chamber will be somewhat misaligned in relation to the threads but it wil be a good chamber and probably as good as possible under this kind of adverse condition. Again, the loose holder/pusher really does work very well in this type of situation and you would simply thread with the crooked barrel aligned in the headstock as well as it could be then count on the loose holder to allow the reamer to follow the wandering bore.
The slightly curved bore is a commonly encountered problem and one which has to be dealt with. The loose holder system probably does a good job of dealing with this more easily than any other method. Regards, Bill

Well, a 6 jaw chuck is nice, but certainly not needed. Any independent 4 jaw will work fine. Through the headstock is the most popular method. Using a steady is kinda old school. Old lathes didn't have a hole through the headstock big enough.

A 4 jaw on the front and a 4 screw spider on the back will do very well. Don't forget to adjust the lathe and tailstock first.

I still use a steady. But recently had to use the headstock as the barrel was too long for a steady.

forgot to mention that I also use a 4 screw spider on the rear of the headstock hole. I have used a 4 jaw and of course it works just fine, but I got a 6 jaw a few years ago and use it for anything except really bizarre shaped pieces that must be offset with a 4 jaw.

I used to chamber off a steady, and it works just fine. However, I screwed up a Krieger and had to eat $275 and went to the headstock after that. Not saying that the steady had anything to do with it, but it is at least pshychologically better for me

Bench Rest gunsmiths are split pretty much 50/50 on headstock vs. steady. It all boils down to what your lathe will handle and how you are most comfortable doing it

Mark me down as "old school". I use a steady rest for all barrel work from start to finish. I've done "through the spindle" and think it tends to make you more relaxed and to take things a little less serious than with the rest. With a steady rest you are always puckered up and watchful. JMHO