Time capsule connected to router configured as a simple, good ol' fashioned hard drive accessible through my network

If you followed an example exactly you probably got the wrong values.

Did you reset to factory as that is important? Do not use the TC with a pre-existing configuration and hope you can just manipulate it.

Start using DHCP.. that way the main router defines the IP address of the TC.

It should work!! If you have issues give us screenshots of the setup from airport utility.

Once you have it setup and working with DHCP on the Internet tab.. you can then swap it to static. All the numbers stay the same except DNS which drops out for unknown reasons. Simply use 8.8.8.8 or some such. This is only to shut the TC up.. the DNS is not in fact needed.

set bridge off

Just to clarify you are setting bridge on.. but Apple uses strange wording.

What is really says is Router Mode ... Off (Bridge Mode) .. meaning.. you are turning off router.. Since this might be confusing they added Bridge Mode in brackets.

I am sure you are selecting the right thing.. just to be aware Apple have always needed to word their stuff uniquely.

To add a bit more.. you could also set the static IP in the main router via DHCP reservations.. whatever it is called.. there are several names. That is jut to reserve the address so only the TC can use it.

I did have to enter the router address which came up empty when I was setting things up

I suggested using 8.8.8.8 (google public DNS)

I presume this is for DNS. Again to state this is to satisfy the TC but is irrelevant to the network. The TC is now a dumb client.

But the static IP helps no end and if you have issues finding the TC in the network.. open it via Finder.. Go.. Connect to Server and use its IP address instead of the name. This is important because a lot of routers do not handle bonjour very well.