Product Listing Adwords Setup

We had a product listing campaign running but spent way too much time and money adding negative keywords each week - it never ended, and Google was sending 70% of clicks our way which we didn't want, they were unrelated products.

I need a product listing campaign to ONLY show our products with one of three specific keywords are in the search phrase.

And then I don't want to have to keep adding negative keywords each week for all other phrases which don't have those specific keywords.

Can you do this?

If you can then I'll hire you to also do some tweaking on our other campaigns ongoing once this is done.