I actually liked your suggestion. I liked the repair spur idea from D Fred. The spur has the benefits that the spur won't rot, but they look a bit rough, but my main concern is that it may be difficult to get the spur & post tight enough to stop sidewards play.
Then I looked at your drawing again, and read Fred's post again and realised you have the join above the concrete.
The spurs that Fred suggested are about 1-1.2m long.....then I thought that there's no reason why I couldn't stick, say, 2.4m post in a 60cm hole, then bolt another 2.4m post to it so there's a long overlap. With good bolts or landscape screws with those corrugated sharp star washers to dig into both posts they should be secure. It might look a bit strange, but the posts could be 'boxed in" to give them a uniform appearance.
I could also box in the concrete spurs to improve their appearance but the concern about the post moving side to side on the spur still remains.
I'm thinking hard about the options, but there's also the option of using the structural timber.
Just an auger drilled hole in the ground to below the frostline, and no need to line it, except for where you may want it to protude. The man powered ones are a bearable effort, but if the stones in the ground are too big to be carried up the screw you end up picking them out by hand periodically.
Also digging lime into the clay will help it deflocculate and let it slowly become drainable, but if it is deep it would take a lot of turning over!
You must have a different vision of the construction to me., sideways movement would be braced by decking subframe , deck boards and overhead horizontals between the uprights.
The bottom of the main upright would be virtually at ground level bolted to the spur behind it which would be under the deck