Just use the overrides system available to you with Zen and tell it to remove the sideboxes on any of the checkout pages.
Instructions for this can be found at the top of the following file:
/includes/templates/[your template directory here]/common/tpl_main_page.php
Do you really make all that much money from your AdSense ads? I mean REALLY enough to keep it in place. If you are making a good amount from it (like MORE than an average sale at your store consistently) then I could see keeping it.
Otherwise, remove it. It will decrease conversion of the site.
There is a place, time, and most importantly SPOT (as in proper placement) for AdSense and similar ad programs. Unless your products aren't of interest to your visitors (to which I would reply, "you would do better finding out and targeting the proper visitor base that wants to become your 'customer' and buy your product) I would remove it totally.
It might not only be the fact that they violate the SSL security, but the pure fact that they are present.
Wouldn't you rather sell your products than make a few bucks from AdSense?
You can make more money with AdSense by placing it on its own site (non-ecommerce) than you probably will on your e-com site anyhow.
Just something to think about.
Finally, just making a change or two to a website and thinking it will increase conversion (checkouts) is usually only going to disappoint. There is a lot more to increasing conversion of websites then just removing an element or two. With e-commerce sites you should have tracking in place (Google Analytics) to record what is really going on, and then test various methods that enhance the overall Customer Experience.
