At least there is some good news. I checked Spectrum Webmail and, to my surprise, all the old emails are there. This, despite it being a POP account. Go figure.
My POP email remains on Verizon's servers until I remove it manually with Mail > control-click on "Inbox" > Get Account Info.
I imagine that there's another way to remove it, but I've got no idea what it may be. Is it a Mail > Prefs > Accounts > Mailbox Behaviors setting, or must I log in to Verizon?