Whatever you need to do to be safe. Personally, I'd try to avoid removing the head stock, but it's not uncommon. I removed the head stock of my old Rockwell 10 x 36 lathe and didn't have too much trouble realigning it.
I'd brace the top of the stringers of your stairs with 4x4's down to the basement floor (vertical columns) as you might be exceeding what dimensional lumber and 16D's can hold. Would hate to see your stairs or worse yet one side come off the 1st floor deck and dump things 8' to the floor.
I moved an Atlas 12 x 36 and Rockwell 10 x 36 out of the basement of my old house. I pulled the motors, tail stock and the carriage. Left the head stock and bed together. I made a plank out of two 2x12x16' as a ramp that set directly on the stairs. Made a couple of side brackets from angle iron and ran a 3/4" rod of steel between the angle, turned down at the ends to fit loosely into a couple of 1/2" holes in the angle (3/4" rod became an axle). That was at the top of the ramp. Made a cart out of 2x4s and plywood with casters on the bottom. Then screwed a buddies 12V truck winch to the floor and hauled everything up by myself. The cable ran over the 3/4" steel rod at the top, kept the cable from chewing up the plank. On top of the lathes, I brought up a Jet JVM-830 mill (900 lbs.), Grizzly mill/drill (700 lbs.), Craftsman drill press and some other woodworking tools that were under 100 lbs. Also brought up an 8' slate pool table (3 pieces at ~150 lbs. each). I have three 10' lengths of roller conveyor too. Use that to maneuver things out into the garage once they were on the 1st floor.
More detail than you asked for, just reliving my move in 1991 . . . Repeating, I'd try to avoid removing the head stock, but whatever you need to do to stay safe. You'll enjoy having a shop on the first floor.
Bruce