Oops, hit send too quick...
I don't know how hard it would be to remove the spider - I think if I were going to attempt it, I'd try a few applications of penetrating oil over a day before I put a wrench to it - I'd bet that the fasteners are probably corroded and there's no worse feeling than snapping off a bolt...and then having to get out the easy-outs and hot wrench.
As far as reassembly, I suppose a person would need to use some care in reassembly so the basket would end up parallel to the shaft so there wouldn't be a runout/balance issue on spin.