This answer suggests that management uri is read from memory in the case of Static Captain. https://answers.splunk.com/answers/339015/search-head-cluster-is-breaking-when-mgmt-uri-has.html
I had similar issues with Static Captain, and instead set dynamic election and preferred captain on the search head I wanted. $SPLUNK_HOME/etc/system/local/server.conf [shclustering] stanza looks like this:
[shclustering]
conf_deploy_fetch_url = **REDACTED**
disabled = 0
mgmt_uri = **REDACTED**
pass4SymmKey = **REDACTED**
replication_factor = 2
id = **REDACTED**
adhoc_searchhead = true
preferred_captain = true
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