I reckon if it was me I'd start with round bar, chucked in the drill press, and 'machined' with whatever you have. Some support might be needed depending how you do it. Then file the square on the part that was in the chuck, or leave enough length to cut the chucked portion off and file the end part.
I sometimes make small guitar parts and other things this way - just 'turned' 3mm pins or spigots about 30-35mm long on some 9.5mm rod, did both brass and silver steel ones. Used angle grinder with flap disc first, then files and sanding. Surprised how accurate I could get with sneaking up on it, and didn't take long at all. It helps that the drill has no or very little runout, so you can see this rod emerging and the straightness etc really clearly.
Not to say go out and buy an angry grinder and plough in, it's not really something to try without being fairly used to handling them, but there's other tools to get there.