I think the ideas that you are considering already would be the way to go. Our product can do "Ignore subjects" and "Ignore email addresses", but it can't do a rule for "allow" so it can't be set to block everything but subjects containing the update keyword.
However, your mail box probably can do this. So if you set a rule in your mail box to only keep emails containing the word "update" and to move everything else into a different folder then Service Desk will only ever read relevant emails. All other emails can still be monitored as they will be kept in a different folder in your mail box.
Doing this in your emails would be the cleanest way of setting this up rather than building this in your process as it would make sure that you don't get redundant records logged from the beginning.
Applying a filter at mailbox would work where it will check that subject line contains "Update:" or not. Either move the mails to other folder or just mention in rule to mark them read and tool will have only mails with Update: word to read and process.
I have applied this in our environment and it worked like charm.