Why am I only seeing results from one search-peer?

[duke_splunk_adm]

I'm trying to confirm that replication and searching can happen on one NIC while ingesting happens over a different NIC.
I have the following simple test setup:

3 indexes in a cluster, each with 2 NICs...
1 master
1 search-head
1 forwarder sending to all three indexers

The search-head is connected to the master and in settings > distributed search > search-peers, or on the command line I see all three indexers in the cluster:

splunk list search-server
Server at URI "dsplunk-index-test-01.oit.duke.edu:8089" with status as "Up"
Server at URI "splunk-index-test-01-private.oit.duke.edu:8089" with status as "Up"
Server at URI "splunk-index-test-02-private.oit.duke.edu:8089" with status as "Up"
Server at URI "splunk-index-test-03-private.oit.duke.edu:8089" with status as "Up"

But I only see results from one indexer when I search from the web GUI on the search-head, or from its command line.

This is my command line search: splunk search "index=* | chart count by splunk_server"
I'm using the same search in the web GUI, just everything inside the "".

If I run the command-line search on the indexers individually I get results from the specific search-peer.

If I run the command-line search on the master, I get results from all three search-peers.

   splunk_server     count      
-------------------- -----                                                                   
splunk-index-test-01   57
splunk-index-test-02   39
splunk-index-test-03   456          

If I run the command-line search from the search-head I get one result.

      splunk_server     count      
    -------------------- -----                                                                   
    splunk-index-test-01   57

If I had configured the search-head incorrectly to the master, I wouldn't see the search peers in the list search-server command results. Or I wouldn't see any results at all. As it is, it makes no sense that one of the 3 indexers shows and the other two don't. Firewalls are all open to the search-head for both NICs on all 3 indexers. I can telnet to port 8089 from the search-head to both NICs on all 3 boxes.

Here's the snippet from server.conf on the search-head:

[clustering]
master_uri = https://splunk-master-test-01.oit.duke.edu:8089
mode = searchhead
pass4SymmKey = $1$7/FK0zLe7w3j3t4lkTuxrXaNBB9vpccQ==

And from the master:

    [clustering]            
    cluster_label = oit                                        
    mode = master       
    pass4SymmKey = $1$bYZ2q5Vu//5VNuiwljjQlH9xYhGBKA==
    replication_factor = 2         
    search_factor = 1   

(pass4SymmKeys have been changed)

show cluster-status shows that everything is up and searchable, all green lights.
How do I get my search-head to believe that it actually should be able to see the other search-peers?