The problem
was only with SONAR, but it's now resolved.
Looks like the culprit was the iZotope IRIS patch I was using to test my initial installation of Platinum. New projects with other synths are now working fine, and even the problem project works fine if I change to a different patch.
If the project loads with the "Keys - Back Rhodes" patch active, everything runs like treacle in winter. But if I change patches and return to that one -- no problem.
So it appears that iZotope is somehow the source of the problem, or some esoteric interaction between certain settings or the plugin initialization, and the Platinum VST3 engine. VST3 is still a bit new for a lot of vendors, so I'll run some tests with the VST2 version of IRIS.
Thanks, Alex & teego, for getting back to me.