I watched your youtube of pressing the shaft out of that pulley hub. A good close fit is needed when running a pulley of that size on shafting. When you make the new shaft, go for that same close fit for the pulleys. I find that using some heat on hubs with as close a fit as your youtube shows makes a world of difference. Years ago, millwrights taught me that when removing a tight-fitting hub from a shaft, put the heat at the keyway. They explained that the keyway is usually the thinnest section in a hub, and putting the heat there will create expansion akin to 'spreading a horse shoe'. Depending on hub size, I use anything from a brazing tip, cutting torch preheat flames, or rosebud. A little heat, properly applied to a hub can make things come apart or go together a lot easier and less danger of breaking a cast iron hub.
When I design and machine hubs and shafting to go in them, I often will design in a 'light shrink fit', even when there is a shaft key. Reason being I do not want to chance having a hub work loose on a shaft in service. The trick to this, particularly with cast iron hubs, is to design the shrink fit to stay well within the limits of cast iron's allowable tensile stress. In a circular or ring shaped part or shell, this is sometimes known as 'hoop stress'. About 40 years ago, I got a bit too generous in how much of a shrink fit I allowed in a cast iron hub when I machined a new shaft. The part (a crankshaft for a small "Marvel" lineshaft driven power hacksaw) had worked loose on its shaft and the journals of the shaft were also chewed up badly. I bored the hub slightly oversized and machined a new shaft, figuring on a shrink fit. I got too generous, figuring only how much the cast iron hub would 'grow' when heated and not figuring the developed tensile stress in the hub. As per the millwright, and 'spreading the horseshoe', the highest developed tensile stress was across the keyway. A crack ran from one corner of the keyway radially to the outer circumference of that hub. Nothing to do but remove the shaft from the hub, machine the OD of the hub and shrink a steel band onto it. Heat the banded hub back up and drive in the shaft with some light hammer blows.
The close fit you encountered with the pulley is a good thing. In subsequent years since the era of your saw rig manufacture, taper-lock hubs came along to insure a 'death grip' between hubs and shafts. Another timeless way to lock a hub onto a shaft is to use a tapered key and cut the keyway in the hub on a matching angle. The tapered key, while locking a hub onto a shaft, can move the hub to take up any slight clearance between hub bore and the shaft. On slow turning machinery, this is usually not a problem, but I've seen a tapered key and flywheel work loose periodically for this reason. On a heavy and large diameter pulley running with any kind of speed, this situation will cause rim runout and resulting vibration. Fortunately, this particular instance had the flywheel running at 200 rpm, and plenty of massive iron around it, tied to a solid foundation.
Even driving the tapered key with a sledge and brass drift did not break it of the habit of working loose. In another instance, I designed a flanged shaft coupling with 'spigotted fit' (male/female on the faces of the coupling flanges). I noted on my drawing that the shaft and coupling were to be machined to a shrink fit and gave the calculated diameters with tolerances. A local machine shop figured they knew better and machined things to a close slip fit. The shaft was about 3 1/2" diameter if I remember right. I was not happy when the parts arrived on the job and was told that was what it was, and the shop said it would work and words to that effect. I let everyone know my doubts. We locked the coupling hub onto the shaft with Loctite 603, I tapped in extra set screws and fitted the key so it had to drive in. In service, surprise ! The assembled coupling started working off the shaft with the 'close slip fit' (aka "wringing fit"). I was asked to do something about it. Only thing to do at that point was take things apart (hanging a chainfall and setting some wood blocking to support the shaft and the big belt pulley on it). I drilled some holes in the face of the coupling and shaft end, at the 'interface'. I drilled the holes as deep as a 5/8" UNF tap could reach, shank included. We then ran some long socket-head set screws in, more Loctite 603, and stacked a locking setscrew against each of the longer ones. These setscrews are tapped half into the hub of the coupling, half into the shaft. Millwrights sometimes call these "Dutchmen". Never had another problem with the coupling hub moving on its shaft. There was good reason I was quite specific in how I designed that shaft and hub. The local machine shop thought they knew better, and it came back to bite us. On higher speed machinery, such as your saw rig, a good close fit or light shrink fit is what I'd be going for.