The key is 100% boycotting all services provided by a company. Wikipedia’s list of Amazon product/services as reference (https://en.wikipedia.org/wiki/List_of_Amazon_products_and_services).
Incidentally, I know entire neighborhoods that don’t have other grocery stores besides Target/Whole Foods, not to mention that AWS is the cloud computing industry standard… As a personal example, my vet-prescribed cat foods are manufactured by Purina, a subsidary of Nestlé (needless to say, a separate but also extremely evil large corporation)
A lot of the time, asking local businesses what they can do/order for you helps a lot. Just because they don’t have it doesn’t mean they can’t get it. Some local grocers offer delivery services. If you have the time, seed money and patience, you can grow a lot of food in a small amount of space.
My cat has a special diet, too. I asked if I could use pet food from an independent brand - since it was a food allergy, just a matter of excluding chicken and grain - and the vet said it was fine.
AWS is harder to avoid, but if you have to use a service, there are other companies who will put the effort in to take part of the pie from amazon.