I dug through all my old A/V equipment and found an unused
RatShack® "Cable TV Amplifier" [part # 1502505, $39] described as 'amplifies a single RF signal'. I had tried it several years ago but it wasn't needed then (I used a Hauppauge WinTV PCI card & supplied cables to connect the TV signal to my PC). I had forgotten I had it, but...It works!

I am amazed!
I have the cable from the street going into the converter box and the output from the box into the amplifier. The output from that into a coax Y-splitter that goes to each TV. Even at minimum gain from the amplifier, I get an excellent signal to each TV. And I can control both TVs simultaneously from the converter remote.
I checked it by unplugging the amplifier. Yuck!
I also connected PC speakers to each TV via the 3.5mm headset ports so I could get independent sound to each TV. Works great!
I am now a happy couch potato!