The most common culprit for the still bug is #2 on Telgin's list. (and not so much a bug as a mechanic) The helmets are in barrel that is currently on its way to the farm to add another mushroom to it. or its actually at the still even after your Repeat job, but is still tasked to go back to the pile before its available again. Or if you bought these then maybe they are still at the Depot, or en-route to a food pile. In addition, If you have a full barrel of helmets and a single dwarf decides to hike 250 tiles to eat one of them then the entire barrel is tasked as busy for the duration of his walk there.
Hundred and one ways for this to happen basically, you will likely never eliminate it completely, but can manage it. I find checking the 'J'obs list to be enlightening, lets you see who has tasked the barrel and exactly why.
I banned barrels in food piles that are inputs for brewers. If you have a version where you can specify the alcohol being made then alternating 2 different drinks on repeat avoids some of this
Fixing the same issue with seeds can be much trickier.
Re: the contaminated caverns. Dont flood it with water, use magma. Not only is it 1000% more dwarfy but water isnt gonna clean up properly, you'll likely just end up with contaminants on the walls of your lake, which never shift. Remember, water pushes the contaminant, magma burns it. And of course if your lake is a real lake (no edge contact) then the gunk is just gonna sit there.
Using dorf-power (with boots/gloves) and decon trenches is a fine idea, but not suitable for all syndromes, some real nasty stuff is just too fast-acting. Also, as above, you'll get the contaminants lodging in the trench walls (unless that's changed with the fixes to waterflow and item-pushing, no clue). Now while contaminants in walls seem to be neutralised (i dont think dwarves can touch it), it still looks messy.
edit: just noticed its your only source of wood, thats gonna be fun, i'd still burn it all tbh, not much else gonna properly clean house.