Problem solved! I had a long tech support session through chat with a Verizon technician from India, and she was excellent. I talked with two other guys on the phone before that, and at least one of them (as I mentioned above) was just dismissive and blamed it all on wordpress; completely useless. Not this Indian technician.
Basically, what she did is she changed my IP address. That solved the whole issue, as now all wordpress pages are indeed loading with no problems.
She did this by taking control of desktop, and then doing a factory reset of the router (remotely; although I did have to restart it manually, too); then she changed the IP. With that, problem solved.
Here's what she told me:
Agent: IPAddress xxx changed.
Agent: There seems to be no other issues, just refreshed the ip address and signals
Me: Do we know what the problem was?
Agent: No major issue, perhaps some signal and outgoing server latencys
Agent: Ideally in future is you wish to know where exactly is the problem you can do a tracert. Let is be any webistes you can do a 'tracert' it will show at which server it has issues.
Me: I did a tracerout - how can that help? What should it say?
Agent: Okay, after you do tracert, you get timed out message below some ip address correct? That indicates that the ip address server has latency, you can check this belongs to which server by using the below link
Agent: Ideally if it is website issue then it will give timed out message
Agent: Then it is simple browser issue.
Agent: Also for future reference only if the tracert gets timed out below 14th hop then you can check with Verizon network else it is onlythe 3rd party server or the website server.
Agent: The above link will show which ip address belongs to which location and their contact details
Agent: Useful for your future references.
Me: Thank you, I will bookmark it. My traceroute stopped at the 8th step.
Agent: Just enter the url or ip in the above link and click search it will provide all details
Not sure how much you can make of it, but the main point is that by changing the IP address, the problem was solved.