Time will tell, but I might have fixed it quite simply. The rubber
wedges that Sharp uses to stablize the whole assembly on the end of the
picture tube had begun to fall out. The tape still held them to the
tube, but the rubber pieces were no longer inserted under the assembly.
I pushed them firmly back into place, adjusted the picture slightly,
and so far (30 minutes), it hasn't made the noise. Here's hoping it
stays static-blast free. ^_^

Baral'heia