MP shopping cart is not responsive

In building a new ecommerce site around MarketPress I discovered (much to my chagrin) that the shopping cart pages and shipping information pages are not responsive and start performing badly at screen widths of 520px and 560px, respectively.

The behavior can be seen in this site:

In looking at the css that is included with MP, it is very sparse (probably a good thing), but the html structure of the checkout page and shipping info page is table-based. Which, to a degree, is probably the source of the problem.

In doing my final review of the build on an android phone, I found the checkout page (the one which presents the option of logging in or checking out as a guest) displayed so poorly that the check out as a guest button barely displayed. When I got to the shipping info page, it was totally unusable. The textbox labels remained anchored to the left of the textboxes (because they are in the lefthand column of the table) when I instinctively wanted them to display above the textboxes.

I see this as a rather significant issue. I can't deploy this responsive website until I fix it, which is going to take some serious time. The other side of this, is that I cannot deploy any MarketPress-based responsive website until I fix it, every time. MarketPress has become a rather mature product and all the other elements (product display pages) adapt nicely into a responsive format, however, it looks like the checkout pages have been a little ignored and left largely unchanged.

While I would like some help in addressing my immediate problem in getting this site finished, should those pages really be built on a table-based layout in the age of responsive design? I know when it comes to plugins, less css is better, but in this case, I'm wondering if the layout of those pages would be better served if it was handle all by css.

Sorry if I'm ranting, but the issue has left me with a rather significant concern to to deal with and I don't know where to begin.