Upon rereading the bit you quoted, I agree that could be an issue. I had initially misinterpreted "all such that a user could run an instance of the service using the Service Source Code you make available" to mean it was limited to any essential supporting bits you had implemented that might have otherwise been made proprietary (much to the detriment of a user trying to actually use the source code you provided). It does seem to be overreaching, but I also maintain that the AGPL has a major loophole as things currently stand.
Edit: From the sibling comment, it seems that SSPLv2 tries to address this.
Edit: From the sibling comment, it seems that SSPLv2 tries to address this.