I think my suggestion is pretty obvious and the devs might have considered it, but if they have not, there it is: When there is an upgrade to a game it's common to have some banners in the front page of kongregate. I don't know what's necessary to make it happen, but I think it could be an nice form of publicity.
Yeah and once the Steam tide calms down, it also it might be good idea to try to get some achievements over to the Kongregate side too.
Mm. Achievements would definitely pull new players in. The banner wouldn't likely affect as much, CH has already been up there before, and they've been the top rated CCG [and one of the top RPGs, and at one point, one of the top multiplayer games] on Kong for forever. So they've front-page presence, anyone who was searching for the genre with even minimum interest would have found the game already. 'sides, adding achievements auto-gets it up on the promoted selection, so, 2-for-1. Just get ready for an even worse flood of spammers than we got with Steam, the Kong-achievement crowd has a rather notorious reputation.
I'm no Kong expert, but I believe the developers have 0 control over what gets pushed to the frontpage or whether or not their games get badges. Actually, a dev could pay a fee and their game would be featured as a sponsored game on the frontpage or something like that, which I think is not what the OP suggested? But as long as badges go, all the dev can do is implement the Kongregate statistics api (which Blue Manchu did) and then it's up to the Kong staff. That being said though, if people really want badges for CH, then they could leave comments and/or post on the CH forums on kong requesting them. It's not guaranteed to work, but it might help.
Games are always front-bannered when they get badges added. As far as getting them added, I don't know. Things have changed a lot since Gamestop took over, all for the worse. It used to be, before, that you implemented the script and the 'hooks' for badges, and then sent in a request to Kongregate. Considering how very rarely games get badges now, compared to the past, I don't know how that's changed. As far as the rest, games are are front-bannered for game promotions, expansion releases, or other events [such as contests]- all paid for and requested by the developers.
Yeah, the 'hooks' part is the implementing of the Statistics API As already stated, I'm no Kong expert (never published a game there, only been an on-and-off user for... 6 years or so?). As far as I can remember, it's always been the case that badges were up to the Kong staff, though I'll admit I never knew devs could fill a form to request them. Pretty sure you can read one of the many guides and FAQs from the developers-area and see the specifics. The thing with games hitting the front-page is every time new content is released, the vast majority of those tend to be either 1) extremely popular (I mean Kingdom Rush/Burrito Bison levels of popularity 2) Games which are sponsored by Kongregate itself. A game getting badges is a sure way to be featured in the front-page slider thingy, pretty much. Paid-for insertion aren't actually that much prominent on the frontpage, and you can easily identify those (can be found on the side, marked as "sponsored listings"). That's the only instance of paid-for advertisement (at least as far as my knowledge of the platform goes), everything else is either curated or based on games' ratings and other automatically-collected data.