To keep n topic were talking front end wiggle (that may, but probably not have to do with riding / engine break /de-cel )
my best guess would be with koko; front steering head proper torque adjustment; then the bearings in the steering head; as per you description at stop with some play (easy to check with one hand on front break and other on triple to frame connections then push back and forth; side to side); and head shaking at de-cel
then front wheel axel shaft proper torque adjustment, yoke bolts and end axel nut; then bearings …
if all that checks then same for rear wheel;
is the rear wheel bent?
then swing arm bearing adjustment;
chain & sprockets
main internal engine bearings
main engine mount through bolts???; check torque on those...eeeks,
... its a little disturbing ; need to pinpoint the issue.... but you know that that's why your posting.