Unfortunately, there's no "super quick" group invite like you're describing. We would love to get a more built-in "groups" concept at some point, but for now your best bet is to use the invite dialog (⌘I, or Room > Invite People). Fortunately, you should be able to autocomplete the names of anyone you want to invite, so typing should be pretty quick.
It looks like there might be a related suggestion (for built-in groups) under https://jira.atlassian.com/browse/HCPUB-313. Feel free to file one more specific to your use case or vote/watch/comment on that one to get updates about any plans we have to implement the feature.
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