YES!
Well I have had a modicum of success here and just wanted to share in case anyone else happens across this thread. You CAN get FULLY COMP cover to drive another vehicle, it's not like I used to have which was all the time any vehicle, but it's the best I think we're gonna find. Here's how to get it:
1. Get a fully comp quote with AvivaOnline. You can get it via GoCompare or similar sites, or direct at Aviva website.
2. Upgrade that policy to 'Aviva Premium', on Go Compare that's a visible option after you get the quote and click to view more details on it. It costs roughly 5-10% more than the original quote. So my standard quote was £350, upgrading to Premium upped it to around £390. (Worth noting it comes with many other benefits like courtesy cars, legal cover, windscreen cover etc etc, but all I want it for is fully comp cover on other vehicles)
3. Aviva Premium told me today on a (recorded) phone call - This gives you 3rd party cover on any other vehicle as normal, BUT if you log into your Aviva online account, you can add any ONE vehicle at a time, to get 5 days of fully comp cover on it. After 5 days it expires, but I was told there is no limit on how often you can do this. She gave an example saying 'if you wanted to drive your brother's car for 15 days, you'd have to login once to get 5 days FC cover, then log in on the 5th day to add another 5 days, and same again for the 3rd set of 5 days.
Only one vehicle at a time, and it auto expires after 5 days, but do it as often as you want.
This is good enough for me and took many hours of screaming at live chat bots and telephone system bots, so I thought I'd make a note here (as much for myself as others!!).