Arcli9ht, cool project.
Two things.
1.) Go back to Home Despot and take a look through the Stairway parts section, they should have long pieces of Solid Oak Handrail, which'll be 1-1/2" or so and oughta be truckloads stiffer'n stronger than pine closet pole stock. But it'll COST a bunch, like dollars/foot. If you're lucky, they might have other material available like cherry or poplar, which aren't any stronger than the oak, but they might cost less. Alternatively, you could also check at a lumber yard and see what they've got on hand. Look in the phone book under "lumber", "Hardwoods" , and "stairs". You might find someone who has something better to offer. A few phone calls are easy to make.
Still another thought is a replacement handle for a shovel, rake, mattock or some other such Weapon of Plant Destruction. These are made of Ash or Hickory, both EXCELLENT, very tough choices for haft wood. Big hardware stores usually got 'em, (I know OSH does. Dunno 'bout the Despot.) they usually run well under $20, (Osh had some for about $7 IIRC.) and they come in a variety of sizes/configurations.
Of course, if you have some woorworking stuff around, you could consider making a thick square bar into something round, but that's MUCHO elbow grease and might require more than casual woodworking ability. Just a thought.
OK, enough about wood.
2.) Unfortunately, that el-cheapo barstock is mild steel. It WON'T heat-treat to any significant degree. It has almost no carbon content, and it simply will not get hard or springy. It won't hold an edge very well either. That's why it's cheap. Don't chop anything really solid with your blade, or it'll bend!
if you want to try your hand at real steel, one of the cheapest sources is an automotive junkyard. Either a big leaf spring, or a fat swaybar off of a big car like a seventies gas-guzzler or a station weapon would work fine, but that once again entails MUCHO elbow grease, as there's some major re-shaping to be done, not casually attempted without an anvil! Leaf springs at least start out flat, but they're usually fatter than 1/4", which would make for a huge slab of steel to deal with.
Grinding spring steel is a bunch harder, too. It's usually 01 steel, which is great choice, but it's virtue of toughness can be a vice of resistance to casual forming. I dunno, if you're happy with the mild steel, just ignore this bit.
If you have a big, beefy-ish right-angle grinder, the easyest way to remove steel is by grinding with large diameter sanding discs that're backed with a rubber disc rather than grinding wheels. 60-grit can cut pretty fast, and you can slap new discs on pretty fast when they go dull. This beats filing by yards, and you don't bleed so much.
Grinding, both with wheels or discs, goes fastest when you apply enough pressure to feel the abrasive biting, but not so hard as to actually slow the grinder down AT ALL.
If you're stuck filing, you're in for some sweating. File secrets: 1.)DON'T run the file backwards. Pick it up on the back strock, or you dull the points quickly. 2.) Keep it clean. Either with a file card, or rub the file with a piece of chalk, or even a piece of wood, to keep the valleys from loading up. 3.) Try lifting the leading edge of the file just a hair as you run the stroke. This concentrates the pressure on fewer teeth at the back edge which lets 'em dig DEEPER into the soft steel. This leaves a rippled finish, but it hogs material off faster. a few strokes with the file held flat will flatten it right up as the hills are easy to knock flat.
I can go on and on. I used to be a machinist, and now I'm a cabinet/carpenter/stairbuilder, and also unemployed! I even have a couple of over-the-top knife projects in the works. (I got a line on super-cheap spring stock for blades. Too small for your naginata, though.) I even have a few ideas about firm blade mounting, if you need some asssistance. Feel free to consult.
