You might want to check out a used Honda Element. I don't know if it would accommodate 2 of the great big crates, but it's a fabulous little dog hauler.
You can completely remove the rear seats (easily, they just unclip and are designed to pop right out and store flat in your garage). You then have a totally flat cargo area with no wheel well. If you occasionally need the seats and want to leave them in, they conveniently flatten and flip up against the wall of the rear area to get them out of the way (this reduces rear visibility though). It looks like this: Google Image Result for http://0.tqn.com/d/suvs/1/0/v/G/-/-/Cargo.JPG
With the seats gone, it looks like this:
Google Image Result for http://0.tqn.com/d/trucks/1/0/-/M/05_element_cargo2.jpg
Best of all, the entire rear area has a textured plastic floor that you can just mop out if a dog pukes in it (just avoid the "SC" trim line, which has a carpeted rear). I am loving having a non-carpeted floor for hauling dogs. It makes mud a non-issue too, after a fun day of outdoor adventures.
It is also pretty decent with its gas mileage, unlike most SUVs and trucks (22-25 mpg, for us). And you get Honda reliability, which you already know about with your Civic. It also drives like a car, not a truck.
Also, there are heavy-duty cargo clips all over to clip in safety "seat belt" harnesses for multiple dogs, which we prefer to crates.
ETA: to avoid jumping in the Element, we purchased a set of fold up stairs. They fold up into a little box, and they unfold into a set of three big, wide carpeted stairs that my old dog and blind dog both easily navigate to get in the tailgate. We found them on ebay, and they are the best thing ever for older dogs.