Tried them both with no joy now
So for the record I haven't changed my AV or Firewall software or indeed any software over the past couple of weeks. They haven't interfered in the past and I'm seeing no evidence of them doing so now. All in the Whitelist, no prompts etc.
I'd be surprised if the ISP was doing anything to it though, I'm on a 60Mbit fibre connection - they won't be worried about the odd API calls.
As for task manager - Minion occasionally (but not always) persists after I've closed it while it's stuck "Loading". On a purely anecdotal level, it seems more likely to persist in the TaskManager the longer I let it run. It's memory useage starts at around 200MB and slowly drops (with the odd wiggle) over time.