Best time of year to move rotting wood piles?

Greetings gardeners!

We bought our place 6 years ago and there were already 3 medium-ish piles of wood that were already well into rot. We don't have a large property, but we are pretty surrounded by trees.

I love these rotten wood piles. They are full of so much life. All kinds of interesting fungi and slime molds, mosses, and we have also found several salamanders. We are also pretty sure we have a generational chipmunk family that has taken residence in two of them.

We have used several of the logs for hugelkuger, but the piles remain large enough to sustain all this interesting life.

The problem is that because we don't have a large property, I want to try to take advantage of all the space I can. We are finally in a good place health-wise and I want to expand the garden and plant more native flowers and trees. And the piles are kind of in the middle of everything.

I want to keep them, but just move them into the corners of the yard where they are out of the way and can still sustain all the interesting and necessary life. I don't mind waiting until next season if that is the best time to move, but I just want to be sure to do it when it is less disruptive.

Winter does not seem optimal because the critters are hibernating and I don't want to expose them and kill them. Spring does not seem optimal because all the critters making nests and having babies. Summer may have been a good time since they would be more active and could better build a new home if I disturbed theirs, but that is done and gone, but I also think that it wasn't a good time because they were likely having additional batches of babies.Now could be good too, since they are likely not having more babies and they are probably actively looking for a good place to settle for the winter, but maybe not a good time because thay may have already built up their food stores and I would be disturbing all of that.

I know there is no "perfect" time since they are going to get disturbed anyway and become vulnerable to predators and weather extremes, but I would like to try to be as least disturbing as possible.

So, what do you all say? Do it now, or wait until next year for a better time?