I'm able to see it now. It seems like there's some work that needs to be done whether or not the pricing model needs to change.
Prorating the first month is ok.. but it should be something obvious for the user. Days left in the month is frequently used, and something you can calculate up front. Which means you won't need to issue a refund later. This (like changing plans and credit card numbers) should be built into the signup/account.
If your plans are cheaper than maxmind, that's not obvious at all. Simply because your plans do not follow the same model as maxmind, and to find out if they are cheaper, I would need to convert them manually to the same units. That could be made more obvious.
I don't think the free plan is obvious enough on the front page. The "Purchase a plan" subtitle under the "See the docs" button could be "Signup for a free account". (Edit: Consider adding a free account so users already have data in your system, and just need to upgrade to a paid account. This will also give you email addresses to market to.)
Am I right that the only way to signup for a plan from the front page is to click on "Pricing" in the header or the small subtitle "Purchase a plan" and then click "Get Started" on the plan? That needs work - "Get Started" should be "Signup".. especially since you use "Get Started" on the front page to go to the docs. IMO, getting to signup from the index should be easier.
Overall I like this service.. But I think your users are right.. the pricing and account management needs to be simplified. These are just my thoughts after a few minutes--you know more than me here, so feel free to ignore anything you think is offbase.
Edit: are there not actually accounts on this service? The pricing page just shows a stripe payment popup. If so, consider changing that.. this could be simple. Ask for email+password, give a dashboard with a few charts (like query counts), a profile, and subscription info. Now the user can login, change their subscription, upgrade to a paid account, and you have their email to market improvements and upsell to.