How can I keep my jam from overcooking while I process it?

If it's getting cooked too much, well, stop cooking it. You can cover it to prevent water loss. If it's too hot sitting on the same burner (on an electric stove), move the pot. It sounds like your cast-iron pot might be part of the problem, too - if it's still staying too hot, you could pour it into something else. Finally, if you do still have significant water loss, I believe you should be able to add a little water (careful not to add too much) and stir and reheat.

P.S. you could also just get a lighter pot. (I know that's not ideal.)

You could avoid the problems by having more jars ready. Here's what I do to get my jars ready.

*When you want to clean jars up for canning, the sterilizing process is between you and yours, not the health authorities.

Here is what I do to clean up my jars quickly. I save jars where the lid acts as a button indicator - if the button is popped up, you don't use it when you bought it in a shop.

First, you wash the jar immediately you empty it in the normal way. Then you put about 2cm to 3cm of water into the jar and microwave it for around a minute, so that the water boils.

Take the jar out carefully - use a cloth or oven glove, it is HOT, and be aware that it may spontaneously "bump" - moving it could cause the boiling water to jump out of the jar, do not point it at your face. Prod it with something long, like a wooden spoon, before you pick it up.

Screw the cap back on. Turn it upside down so that the hot water contacts the inside of the lid. If the water leaks out at this point, don't use that jar - the seal would be OK in an industrial process, but it will not be useful for this trick.

Stand the jar on one side until it cools, add it to your collection.

When the time comes that you want to use the jars, pick out enough to do the job and repeat the boiling out process once again, being sure to only use jars that have properly sealed - the button pops up again to tell you the seal was effective, something will grow in the water if the job was not done right.

Then you make the jam or chutney to put into the jars.

This way you never become short of jars. If you do not pick out enough, it is the work of a couple of minutes to make another jar ready. If you pick out too many, you can put the surplus back into your stockpile.*

If it makes you feel more secure, you can use the solution for sterilizing baby feed bottles to immerse the jar lids during the process, but you must rinse off that solution before you re-fit the lids on the jars.

Wet heat kills more bugs than dry heat ... this way, it is a matter of moments to have extra jars ready - or more than you really need, you don't waste any sterilized jars.

I've taken to using this trick so I can use portions from a jar of, say, pasta sauce. When I use half the jar, I microwave it for a minute and put the lid back, then stand it to cool before I put it in the fridge.

Not properly and fully tested as a method, but I've been doing this for a year now without ill effects.

Why are you boiling-filling-boiling again? Check out canning myths. Trust me it’s there. I simply run my jars through the dishwasher checking for any possible grit after (we’re in a farm so sometimes get a silt/sand in the bottom of cups) turn the jars upside down on a towel while making jam. Fill bottles with pipping hot jam screw lid on tight. Turn upside down. Then go relax till fully cooled or 24 hours. Turn right side up push center of lid might click down (and stay down!) your good to go. Lol no batch of home made jam that fills 2 pint jars ever lasts long here. But I’ve been told by my grands at least 6 months possibly years. Just push the center of the lid every so often. Once opened as long as there’s no mild and smells like jam I think you’re good.

We do a haywire canning spree every once in a while. Never had a problem and the ones that don’t take are easily spotted