Currently in discussions with a chrome expert.
Chemicals (DIY) are out - as has rightly been pointed out - very high probability of 'eating' the spider.
Powder coating is out - (at least not until the chrome has been removed) as several powder coaters have stated that they deal with chromed parts by etching the chrome and powder coating over the top. Almost certainly, this means the spider will not fit onto the crank. I wouldn't go so far as to say it is a compression fit, but it's damned tight - without a layer of powder.....
Interestingly, the spider itself appears to be no magnetic, but at the suggestion of the chrome expert i peeled off a couple of very small flakes of the coating - which are highly magnetic when not attached to the aluminium.
I don't understand the complexities of metals, but that's where we are at - establishing what the coating actually is.