Some cheap V belts have a swollen area near the join.
Good quality belts don't. A lumpy belt will cause a slight variation in speed of the Mandrel, which will not help your problem.
Looking at the tool that you ground, it has a flat on the corner where it should be cutting.
A Knife tool will have a sharp corner. By very slightly stoning a radius, as said, all the way down the edge, the finish will improve.
But start with a SHARP corner, before trying to stone a radius.
The radius must extend down the edge, or the tool will rub rather than cut. For the tool to cut, the pressure at the point of contact must be great enough for the metal to shear. Hence the need for an almost point contact, to give minimal area to support the applied load, and produce high pressure..
I use a Tangential turning tool, and don't bother with a radius, since a fine feed, circa 0.002" (0.05 mm ) per rev produces a good finish on steel or brass.
But that's just my preference!
Whatever tool you use MUST be on the centre height. A quick check is to face across the end of the bar. If there is a pip in the middle the tool is not on centre height, and needs to be shimmed up or down, until it is.
Once you get the tool on centre height, it would be worth making some form of Centre Height Gauge, so that in future, all tools can be set to it, Making it will be useful learning exercise in itself.
It might be worth when the bearing bolts have been set to provide acceptable rotation of the Mandrel, to measure the clearance between the caps and the Headstock, and then to make up shims so that the bolts can be tightened down onto the shims to limit the "grip" of the bearing. There needs to be a minute clearance for lubrication, say 0.001" (0.025 mm ) but excess clearance will impair accuracy and surface finish. On a lathe of this vintage, lubrication will be drip feed no doubt, and should be operated at relatively low speeds (Hundreds of rpm not thousands!)
HTH
Howard