First check your tyre pressures are correct and the tyres are in good order.Put the bike on the main stand and check the rear wheel bearings (You Tube or Google to save me typing it all out)Then check the swing arm for play, up and down plus side to side.Get someone to lean on the rear of the seat (while on main stand) so that the front wheel is off the floorCheck front wheel bearings for playGrab the bottom of the forks to check the steering stem bearings.If nothing obvious check all discs for run out and sticking pistons in the calipers.
I wonder if you've got wheel shimmy darrsi? Could be the tyre just needs balanced, check the condition of the rims
Probably a daft question but are all the shock and dogbones bolts torqued up/ tight and no cracks in the coil spring ?
I'm sure a decent shock will be an improvement even if you don't find anything wrong with the linkage, but it's possible that temperature has a lot to do with it.The first 8 miles of my commute to work is on slow twisty roads with plenty of undulations, pot holes and long shallow depressions where trenches dug for pipes have sunk after repair. It feels similar to your description: a jarring ride and I keep thinking the back end's trying to step out.OK, I've a knackered shock and the rear tyre's beginning to square off, but in winter there's a huge difference in how the bike feels in the morning when the tyres (and shock oil) are cold and when I come back at night after a long blast down the M4 and they've had a chance to warm up.
Have you ridden it since? Does it still feel the same? I had what sounds like a very similar experience a week or two back while out for an afternoon ride. Sort of feels like your riding on a flat tyre? Every corner felt like the tyre was folding under the rim? Put me off so much I had to come back home as I was convinced I had a puncture or a bearing was shot but couldn't find anything wrong and has been fine ever since? Was very strange