Hello Alex,
Another possibility might be a shallow bruise on the chamfered mouth ot the chuck register if this trouble was confined to only one item. But as it appears to be across the board then I go with the others on the thinking of fine embedded swarf now incorporated with the spindle thread.
A suede brush with brass wires might shift it, a little kinder to use than a standard wire brush. I would use taps on chucks only with reservation, a threading nut on the spindle would be best avoided I think.
As Chris says, don't force it on, big mistake. A little moly grease on the spindle thread might help ease things a trifle but look out for it breaking down and allowing 'pick up' in metal to metal contact, leading to a seize.. It it feels tight with moly grease, undo it pronto. The grip on the thread should NOT be that tight, the register does the alignment.
I hope you get it sorted out satifactorily
Brian.