dschad:
The flypress and blocks are a good method to start off with for cold straightening. A little at a time, nothing drastic.
I would NOT heat the spindle up until it is "plastic" (red hot) to work the bend out of it. Using the "blacksmith method" will wind up with more problems (experience talking here) for straightening a shaft. It is one thing if you are straightening a bent chunk of bar stock or a bent pinch bar, but quite another when we are talking small amounts of movement to get something like a drill press spindle straightened.
Flame straightening is quite precise. You will need an oxyacetylene torch with a small brazing tip to apply very concentrated heat in just one spot at a time.
There are two excellent youtubes showing flame straightening, one by "Turnwright Machine" (Fenner), and one by Keith Rucker. Rucker uses the method I'd use for the drill press spindle straightening and gets things within a few thousandths for runout when he calls it "done". He does the straightening with the part (the arbor for a woodworking shaper) chucked in a lathe and uses nothing more than a plastic tub of water and a sponge to douse the areas he has heated. Little by little he draws the arbor into true and gets rid of a bend (or very nearly so). For something like your old drill, this would be more than adequate for repairing the spindle.
Do NOT use the quill to force the spindle back to straight, whether doing it hot or cold. These old drills often had no bearings in the quills, but relied on the quill being made of cast iron. The cast iron quill was bored to create two bearings, with cast iron being an excellent bearing material in its own right. The spindle journals ran right in the bored fits in the cast iron quill. Some other of the old drills used pressed-in bronze bushings. Ball thrust bearings were commonly used with some adjusting nuts to set the end thrust or preload.
Using the quill as a forming die or similar is not going to work. My guess is the bend happened somewhere just above the crown gear. I'd leave the drill assembled with that bad a bend in the spindle, and do a preliminary flame straightening in place. You will not be putting enough heat into the spindle to travel far enough to hurt anything, and you will be rapidly cooling the spot)s) you heat for the flame straightening.
My thought is to take any guards or similar off so the crown gear is exposed. This is where it gets a bit crude, but for rough straightening in place, I'd place a carpenter's framing square on the top of the teeth of the crown gear. With the square spanning across the gear the other leg of the square is approximately vertical (or should be parallel to the spindle if the spindle were straight). Using the square as a reference, see which way the spindle is bent. Another method is to rig up some kind of fixed reference point such as a piece of lumber or steel flat bar clamped to the drill's frame. This reference should be fairly close to the spindle. Roll the spindle around and you will see which way the spindle is out relative to your reference. A good eye is what it takes at this point. Once you have determined which way the spindle is bent or cocked, get the torch and a container of water and some rags and do a preliminary straightening. It may take a few times, and do not heat more than a spot perhaps 3/4" in diameter on one side of the spindle only. The object is not to heat a complete band, and we are not looking to "hot work" the spindle by bending it when it is at a "plastic" heat. Rather, we are talking of using the contraction of a locally heated area to pull the spindle back into straightness.
After the preliminary straightening, you should then be able to dismantle the drill and do a final straightening using flame straightening and dial indicators.
It's a case of "metal magic" rather than brute force or blacksmithing.
FWIW: About 25 + years ago, I bought a used Cincinnati-Bickford 25" Camelback Drill. It was in excellent shape, just covered in grunge which acted as a preservative. It was built with a factory motor drive and has an original 3 HP GE repulsion-induction motor, an old heavy-framed brute of a motor. All the oilers were intact, one or two stray holes in the table and no broken or missing parts. I paid 200 bucks. I spent 65 on new brushes for the motor (Helwig Carbon, an excellent source of brushes for the odd and ancient motors and generators and they know which carbon composition works for which application). I took a piece out of the leather belt as it had gone slack, and cleaned the drill. All the working parts are nice and crisp. The thrust bearing on the spindle had gone south, so I replaced it with ball thrust bearings top and bottom. My Kaman distributor fixed me right up for maybe 9 bucks a bearing as I recall. I've been using my camelback drill ever since.
I have no idea what camelback drills are fetching nowadays, whether collectors have driven the prices up. However, you are in New Hampshire, not what I'd call a "desert" for finding old used machine tools. If you were in a place like Taos, New Mexico or on an island in the middle of an ocean, I'd say this particular drill might be more of a "find". It comes down to how bad to you want a camelback drill, and are you prepared to pass on this one in the hopes that something better comes along. The gamble is you might wait quite awhile, and maybe not find a camelback drill at all. They do have a way of turning up, usually in the back of older shops or truck and farm machinery repair or fabricating shops. Regular machine shops have gotten rid of this type of drill a long time ago. My camelback drill came out of a heavy truck repair garage that was so old that it had started as a business building bodies for horse-drawn wagons. I got a few blacksmithing tools along with the drill, as I was the only one who seemed to know what they were.
Royersford was probably the last builder of these drills in the USA. I believe they were building them at least into the 1970's or early 80's. They built a lot of them under the "Excelsior" name or under their own name. A buddy of mine was given one by an oldtimer. It is about the closest thing to a factory-new camelback drill I have ever seen. It saw little use and the oldtimer was the original owner. He put a single phase motor drive on it and apparently did not use it much. Sometimes, these things fall into your lap, and sometimes no matter how hard you look and want them, there are none to be found.
I had given up on getting a camelback drill when I had occasion to be in a shop where we'd ordered a new body for a service truck. There was the camelback drill sitting, unused, out under a kind of lean-to off some shipping containers. I asked about it and was told "not for sale". A couple of months later, I got the word that the truck body shop was "consolidating its assets", so showed up with 200 bucks and got the drill. I knew of its existence and kept my ear to the ground. A fellow who knew that truck body shop knew I'd asked after the drill and got hold of me. I was lucky in that the camelback drill I got was in fine condition with little else needed to put it into good operating condition.
It's a roll of the dice as to whether to pass on this particular drill or grab it.