Sienna has a burping problem

My 200 Sienna is doing something I call hesitating… only when cold and only when the car is under load, like going up a hill or accelerating onto an interstate. It sounds like the engine is disengaging or skipping or something. No codes appear.

These are the things I have had done: new timing belt, new spark plug wires, new MAF, and assorted tuneup stuff (plus new tires and battery (which don’t count, I think.

Problem started about a year ago with a huge backfiring episode. I have taken it in at least 5 times to two different mechanics, one a dealership. And the check engine light never comes on.

HELP!