Sam's suggestions are good and I think testing what constraints or premium experiences you can tease in the product experience itself can lead to some increases in conversions.

My advice would be to A/B test the copy on your premium page. I'm not a user of your app (but I understand what it does) and the way you describe the premium benefits just don't feel too compelling. Some small copy changes could result in increases in conversions.

Some social proof (pictures of customers with testimonials or even just testimonials) about how much better the service is with premium could really help.

Also, I hope you're already using analytics to determine how many people click on the "Get Premium" button but who don't complete the purchase. My sense is that the multi-point purchase plan might be leading to fewer purchases. You might want to experiment further with fewer plans or a fixed plan.