We lost track of the venting time but since it was a strong heavy steam, husband put the weight on. Regulating the jiggles was hard to do and finally we just turned the heat off. Thinking to start over. We opened up the canner after it set an hour. Opened it, pulled the jars out. But some of the jars started to ping. Must we open them up, and put new lids on? Or can we put the jars back in to reprocess as is?
Official advice (which is the only sort here on food safety issues) is to empty, and repack into a clean jar with a new lid.
But why? It sealed, and I'm going to process it more?
Because the processing times published are (usually) based on the hot jars being packed with hot food, not room temperature jars of food being subjected to heat. Particularly with any thick pasty food, the center of the jars may not heat adequately from "just reprocessing" and the odds that your family will show up posthumously in one of those cautionary tales about doing canning wrong go way, way up...
Sealed is NOT "safe" if the path to sealed was not the path in the tested safe recipe.
While most "reprocessing" advice assume the seal failed, failing to maintain the time/temperature as specified in the tested process is a path to jars that look sealed, but are not safe. Reprocessing them without emptying, reheating, and repacking is likewise unsafe.
You describe a pressure canning process.
Jars seal just fine in a boiling-water or steam process at much lower temperatures, which will result in unsafe food if following a recipe intended for pressure canning (low-acid.)