How do you plan to confirm that the different websites deserve the awards that are being given out? Why would someone trust that your website gives out the correct awards to the right websites? There is some general wording about this already on your website but I would try to get more specific on what the criteria is.

Also, if the badges have "AwardIn" on them and someone googles "AwardIn", they're going to see that the award comes from a website that gives out awards for money which then cheapens the value of the award.

I think to your point about conversion, ideally you should prove that in some way - i.e. get some data from people that have signed up for badge and do an A/B test on their signup flow with and without the award and see how much the conversion improves, then do a writeup about that and add it as a blog to improve your SEO.