Sticky, messy sourdough: overfermented, or ambient factors? I've made the same sourdough bread a dozen times before, with small variations in parameters:

360g white flour
240g whole wheat flour
390g water

That's a 65% dough with 60% white and 40% whole wheat flour. I've been using the sponge method wherein the night before baking, I'm mixing half the flour (300g) with the water and 60g stiff (100%) sourdough starter.
The next morning I mix in the rest of the flour, 2% salt, and knead by hand.
This has worked well throughout March-May, but the last two times I attempted it I'm having trouble with dough that is sticky, stretchy, and a nightmare to handle.
Last time I ventured for 70% hydration and 1:1 white to whole wheat flour and it got very messy and I abandoned it.
Now, when I'm sticking to my tried recipe, I'm still having the same issue:

No matter how much extra flour I incorporate, the dough will not become more manageable... it seems it's ready to swallow an entire pack! 
Do you think it could be:

the sponge, which was left at room temp. for about 10hrs, is overfermented? (I don't have a picture, but it looked normal, bubbles like a tapioca pudding, no signs of hooch)
the ambient humidity has messed up the recipe in a major way?
a combination of both?

It's warmer (25C) and wetter (55-65%) here this rainy June as opposed to ~22C / 40%.
If the sponge is overfermented, does halving the starter help in any meaningful way? Or should I give it less time?
If the flour has been soaking up water in the pantry, how much water should you add to get a predictable result? Do I just weigh a pack of flour and work out how much extra water it holds?
As for The Blob, do I continue to incorporate flour into it and hope it starts holding shape, or does an overfermented sponge preclude me from getting a decent loaf?
Update
I've been using the same brand of white and whole wheat flours throughout. Nothing substantial about the technique has changed. I knead the bread by hand 10-15 mins through a series of smear-scrape-twist motions, as shown below in the River Cottage Bread Handbook:

65% hydration with 60-40% flour mix was my safe space, and the dough just doesn't seem to come together as of late.
This is a bit unusual, but from your picture, I think your long rise at a high temperature (25C) has indeed overfermented your sponge. It's not so much that the yeast is used up: in fact it might still be active. The problem is that the gluten that developed in the first few hours has been broken down in the long fermentation. Hence the lack of structure. You can't fix this by adding any small amount of flour.
Instead you could use this dough as preferment. Then you will need to add plenty more flour and water (maybe matching the amounts already used) and knead again, or use a no-knead rise (but not 10 hours) to develop gluten.
A method for finding the moisture content of flour that's practical in a home kitchen is suggested here: https://bakerpedia.com/processes/moisture-in-flour/.