I hope you will not give up on something that obviously means so much to you. One other thing you might try is to get a room air purifier to run in your sewing room. May not take care of all the smoke and pet hair but, they do help. My husband and I have allergy problems and we have one in our bedroom. Amazing what the filter looks like when I clean it. (Don't forget to clean filter frequently) Just one more idea to try. Never, Never give up on a DREAM!!!! Good luck and God Bless your endeavors.

Smoke odor does wash out.

I can't understand why someone would take a bath, wash their hair, brush their teeth, put on colone ALL to smell good and then light up a NASTY CIGARETTE

I used to play bingo and in the large bingo hall there were smokers. When I came home, my husband could always smell the smoke on me. I was even in the non-smoking room too. My hair smelled like smoke, my winter coat........had to wash my clothes and take a shower and I let my coat air out before I put it in the closet. I am sure glad I live in a state (IL) now that doesn't allow smoking in restaurants or public places.

Because you really don't realize how bad you do smell. I am an Xsmoker and I didn't know. Now I cannot stand to be close to a smoker. Is NASTY and STINKY.

I have asthma and I can tell when the slightest bit of cigarette smoke has been near fabric. I had to stop going to the craft shows because I have a reaction to the smoke.

Good grief, people! There's no need to be so RUDE!

Attitudes can be stinky, too.

I used to smoke. I got a forced air heating system installed. I smoked only in the family room, thinking one room was ok. But the smell would wake my DH in the early mornings, so we decided to only smoke outside. I was always aware which way the breeze was blowing so I stayed upwind of the smoke. Clothes still reeked.
Got a haircut one day, they used deionized water to rinse it. They told me I must be a smoker since the smell was literally emanating from my scalp.
Didn't smoke in my vehicle, yet there was still cigarette haze on the inside glass--from breathing out the residual that was always left in my lungs! Whatever I breathed on was exposed to cigarette smoke.
Was in a quilting group for many years. One dear lady started to bring a neighbor with her, a smoker. She took a butt break every 20-30 minutes & never washed her hands. She reeked SO bad I had to just leave if she came.
We quit smoking going on 6 years ago, never thought we could after over 30 years. Nicorette patch made it literally effortless.

In your climate, you can get the fabric very dry in the dryer, let it cool, and store it folded in a very roomy large plastic sealed bag. You probably will not plan for it to be in there for a long time, but it will keep it fresh and clean.
I have had some quilts in large roomy plastic bags for over a year, some longer, with no bad results.
It is certainly is better than letting smoke smell get into the fabric, because trying to remove the smoke smell, could be harder on the fabric.
It is moisture in the fabric sealed inside a confined bag in a warm humid climate that can do the damage.,
After all - archarologists have found bits of fabric several thousands of years old, that have been in a sealed dry place in a dry climate - like your house inthe winter time.
Jeannie

I agree with the advice to give it a go and be honest and up front about being a smoker and having a cat. I'm sure that there are a gazillion smoking, cat-owners out there. Good luck.