Failure to record one channel and watch another might happen in a single cable setup.

Check your cables for sound mechanical and electrical connection.

There’s some ambiguity about your symptoms.

You say “both feeds have a strong signal, and when the feeds are swapped all channels still work.”

How are you testing this ?

Signal quality is probably more important that signal strength so focus on the quality report.

How is your dish LNB connected to the HDR ?

Dual cable, single cable with loop or single cable without loop ?

Your post suggests two cables – if that is the case confirm that the box is set for dual cable.

A test for functional dual cable and dual tuner operations is to

1) Start a recording an H channel – occupies one cable and tuner 1

2) Start a recording a V channel – occupies the second cable and tuner 2

3) Watch another channel – choice will be limited to one on the same polarity and frequency of the recordings being made.

From what you’ve posted, you would fail at step two.

Even on a single cable with loop you should be able record a channel and watch another (provided it is on the same polarity and frequency as the recording).

If you can’t watch anything, it suggests tuner 2 has nothing connected to it which is contradicted by what you’ve said about all channels working.

You may have two or more problems, but your main symptom suggests LNB/cable/tuner/set up rather than hard disk.