Having done some research, I know a bit more now.
The CathInfo server is actually 3 1/2 years old (which is fine; the server isn't the problem) but the router is just as old. I wanted to know if they make better ones (more CPU, more RAM, to handle more connections per second) in the last 3.5 years.
Turns out, they do.
https://shop.asus.com/us/90ig08g0-ma1a0v-rog-rapture-gt-be98-pro.html* I know the server is fine. Pages are created near-instantly on my end. The server isn't running that hard.
* I know my Internet connection is fine (300 Mbps up/down) because I can do whatever I want on the Net with no slowdown. So my Internet pipe isn't clogged.
So my best guess is that the router is slowing things down during the forwarding of traffic from the "entrance to my house" to the CathInfo server.
I could be wrong, but that is my best guess.
From what I know about computers (and my knowledge is quite broad, and sometimes deep as well) it is possible that port forwarding work is done by just one of the "cores" of the CPU. So the faster the cores are, the faster that traffic can be processed.
Also, it's possible that ALL the memory of the unit can't be dedicated to "active connections on the router", although in an ideal world it would be.
So if you double the RAM, chances are, the manufacturer's engineers would (hopefully) increase whatever "setting" limits how much RAM is allocated to port forwarding.
Just an educated theory.
This router has a 2.6 GHz quad-core CPU, and 2 GB of RAM.
The existing router has 1.8 GHz quad-core CPU and 1 GB of RAM.
TL;DR -- this new router is $630. So if someone wants to help out with this, I would be happy to install it.