I've read the whole thread and am puzzled.
Bacteria cause a smell on people when they react with sweat and this smell can pervade clothes of course.
But the bacteria are not on the clothes themselves to cause a smell?
www.antiperspirantsinfo.com/en/all-about-sweat/why-does-sweat-smell.aspx
The smell is caused when the bacteria on the skin mixes with the sweat/ gunge from our apocrine glands ( see link)
The bacteria are probably inactive once the garment is not being worn because it's body bacteria that causes the smell.
The whole point of washing clothes is not to get rid of bacteria- there are billions of bacteria in the air and on us all the time and the minute anything is taken out of a washing machine bacteria will land on it. But they aren't the bacteria responsible for smelly sweat- they live only on our body under the pits, groin etc.
The solution is to use a good enough antiperspirant to stop the sweat in the first place, but if this doesn't always work, wash the clothes on a hot enough wash to remove the residue of sweat and stale antiperspirant.
As apocrine gland sweat is greasy ( see link) then a bio laundry product is going to be best and a hot wash. You don't need do anything to 'kill' bacteria.
I also think OP that you may be overloading your machine. This will limit the agitation and may mean clothes are not getting a good rinse.
I am sure I've read that a decent load is 6 shirts and that any items that are mixed fabrics ( ie polyester and cotton) should have more space in the machine .
I'd never mix loads of items: mine usual mix is 2 bath towels, a small guest towel and a bath mat as one wash on 60C, a set of undies and socks as another ( maybe 6 pairs underpants and 6 pairs knickers and 6 pairs socks; half a dozen shirts ( 100% cotton) as another wash.
Bedding is one king size sheet plus 2 pillow slips as one load, one king size duvet cover as another load.
I've got a mid-range Miele machine which uses the right amount of water for the load as it weighs the clothes.