UPDATE:
First, thanks for all the suggestions.
We are back home now after over 7,000 km. We couldn't replicate the problem, but knew it was something more than just a shudder or misfire. It would momentarily stop, but before I could pull over, it would go again. It is high mileage (300) and has never had work done to it, and not wanting to be stranded, I took the plunge and had a new transmission installed. We were at what seemed to be a very competent shop and they agreed to do it immediately because we were traveling. Trans temps were mid 90s C before and the new one runs 40s and 50s C. Very costly, but buying/selling/trading/renting weren't reasonable options for us at the time, being out of country.
HOWEVER.... after all this, the problem recurred a few hours down the road. This time it triggered a code for fuel pump issues. My wife googled the code as I pulled into a gas station for fuel. It said common in high mileage vehicles, especially when low on fuel (when the pump isn't submerged for cooling). Both instances were when it was at 1/4 or less. By this time I had refueled so we took off. Never let the tank get below 1/4 tank again and no more issues.
So, I expect to replace a fuel pump shortly, and sort of wasted $$ on transmission. However, the dramatic difference in trans temps tells me it may have been on the edge of giving trouble soon, too.
