Explain to your husband that visits to the Emergency room = $$$$$. Air borne wool fibre can irritate people with these sensitivities and can lead to long term health problems. People with eczema often have breathing/lung issues (not always...but it is common to have both). Exposing people with wool sensitivity to 24 hour wool is a recipe for expensive medical treatment. Synthetic fibres are your best option if you must have wool. Solid/hard surfaces are much better/easier on people with sensitivities as they reduce airborne particles and allergens. Hardwood or cork would be a much better choice for air quality.

I was about to say grey until I read the last line. What about a light brown carpet?

You could always use rugs/area rugs to make the family space more cosy :)

I think the brands you have listed are good! What colour were you thinking? How have you gotten the opportunity to import carpet? I hope it's not too expensive for you!