Greetings,
My name is Ryan, I work full time for a web development company in Arizona, USA. I have expert knowledge in SEO , and Site Speed Analysis. I have in my past taken desktop and mobile site speeds from a score of 20 all the way to the high 90's. Alot of times in this situation, especially with wordpress, ecommerce sites tend to utilize a lot of javascript, non-blocking javascript, as well as large images that are not cached. I propose doing the following, to update your score of at least 30 + points.
1. Optimize non-blocking javascript, means loading javascript that is not necessary to load in the footer to allow the page enough time to load.
2. Cache large images , and possibly utilize a CDN to reduce page speed for larger images.
3. Cache and minimize javascript, and css elements to help the site load faster.
These are just a few things that I will target first, but as I said , I have a fully tested workflow for increasing site speed score, and have worked with clients for over 5 years.