Peter,
"I'd been using the pistol insert, so that wasn't an issue."
Actually, this may be your issue, depending on the powder. I would try the rifle insert and see how things go. I've found many pistol powders work much better with what they now call the Rifle Micrometer insert. If you have the standard rifle insert, try that and see how it goes.
"I wasn't aware of the need to lube the measure, but I imagine the moving parts and places where the powder flows would be where I would. Can I use Hornady One-Shot for lubing? If not, are some dry lubes better than others?"
With most powders you don't, but Clays doesn't have any graphite in it, so you'll likely need to lube the press a bit to help it go through. A little bit of powdered graphite or mica in places where the powder goes through should help. Don't use much and empty it out. You just want enough so the powder slips through freely. Hornady One-shot case lube will do fine in areas where the powder isn't traveling.
"I cleaned the measure thoroughly with brake cleaner before I used it, should I re-clean it?'
No, you should be fine.
"Since everyone but Hornady is o/s on the pistol drum, I guess it's off to Oroville and RCBS for the powder baffle. I'll let y'all know how this works."
I don't think you need the powder baffle. I think the pistol insert is probably your problem. Try using the rifle insert and see how that goes.
Regards,
Dave