Hi Justin,
I have also gone through the same case that you are exactly facing now now I'm telling you how I handled this.
I have started PPC campaign with purpose of keyword research and search volume so I have started with very low daily budget and my aim was to appear on page one only at (e.g position 5-7) because I don't want users to click on my ad frequently, just wanted to know the number of impression for each keyword.
I have run campaign for 3 months and I spend less that $100 and I got several new keywords to target with high search volume and low competition.
So If you can run campaign only for new keyword research that will be helpful for you and it won't cost you much.
I presume you are aware of search term list in Google search console (Google webmaster tools).
If you have semrush paid account you can find organinc and paid keywords of your competitors and many more things.
I'm sharing one article how can you use semrush tool effectively.
http://www.robbierichards.com/review/competitor-research/
Hope this helps you.
Thanks