You really don't need the water very soapy at all. In the past a good soak was the most common way of pre cleaning, and wool's no different now than then. Just be gentle with it.
Soap is alkaline, and that's not really ideal for wool, which is why I said to use the shampoo or the Ecover stuff.
Not even enough to make a lather is a good guideline to quantity and let the garment sit in the water overnight......those £5 garden trug buckets are brilliant for it

, but the bath is very good and has the advantage of letting you move things gently in the water to dislodge any dirt, and allowing things to drain without wringing out
Rinse well, add lanolin treatment or conditioner as chosen, drain again and squeeze 'very' gently.
Then lay out on the biggest towel you can find, roll it up with the garment supported by the towel and you can wring/squeeze well.
The towel (because it's cotton, and cotton is 'thirsty') will soak up a tremendous amount of water from the woollens, and the woollens can then be laid out to shape and left to dry. When almost dry a coat hanger inside and put it outside to air and finish off.
No harm, no foul, just cared for and will last for years
Modern machine washable merino is brilliant, but it doesn't seem to last anywhere near as long.
As for modern ingredients messing up the wool......no, they don't. The chemicals used to prepare the wool in the first place, and those used in the knitting, weaving and dyeing processes are far, far harsher.
cheers,
Toddy