First off not only is soda bad for children, diet soda is the worst. The chemicals in them have been linked to autism, adhd, migraines, many other behavioral disorders and worst yet, cancer. Even only once a week is bad. You are setting him up for unhealthy habits later on in life.
Second it is not bad for him to chew his food for a long period of time. Saliva is essentially digestive juices and he is breaking down his food. It would be different if he was refusing to swallow at all.
Also our mouth absorbs some of what we put in it so he is still getting nutrition, it just isn't in the form you want. Allow him the extra time to eat and let him have a drink with him at meal time. I know that sometimes I want to wash my food down, we all do.
Food also is an area that kids learn they have control. You can't force them to eat something they dont like no matter what and he seems to know who is in control at meal times, he is. He knows it makes you frustrated so repeatedly asking him to swallow only fuels that. Then you offer him soda to swallow. He has learned how to get what he wants.
If you want to turn this around, start ignoring how long he takes. If it means he can't go somewhere, tell him, "If you don't eat quicker, we won't be able to do x" and then stick to it. If you all sit down to eat together, don't wait for him to finish. Tell him "We are finished eating now so we are getting up to do x" He may not want to eat all alone and will finish so he can join the family.
If you still feel you want to give him a drink as a treat, try seltzer water and juice. Much better for him and it fizzes so he will still get the effect of soda without the health risks involved.
Best Wishes
J.