Heel-strike while pedalling a new road bike

I'm in the market for a new road bike. My purchase is imminent and I'm very excited to have a road bike that I will use for racing and training. I currently have a hybrid that I use for trail riding and commuting. I plan to keep the old workhorse and just add a race horse to my collection. Since this will be my first road bike, I've decided to be sensible about its cost, and I'm only considering the entry-level bikes that typically cost $1000 and feature an aluminum frame, carbon fork, and Shimano Tiagra components.

I've gotten a lot of feedback from friends and fellow bloggers about how to go about choosing a new bike. The overwhelming majority of folks said "you just have to test-drive a lot of bikes and choose the one that feels right." While this sounds like excellent advice, in practice I have found it quite difficult. You see, I'm 6'4" and none of the three local bike shops near me had any bikes with a 60-62 cm frame that my body size requires. One bike shop is already out of consideration because they really couldn't get me much bang for my buck compared to the other two shops. One bike shop was really awesome and has worked with me several days in a row to get me a bike that fits. After my initial visit, they ordered it and will add it to their inventory if I decide I don't want it. After taking my measurements and adjusting the bike to fit me, I took the bike out of the shop and rode it around the neighborhood for about a mile. I really want it! But I put off the purchase for one reason: I found that my heels bumped into the chainstay (interestingly, just on the right side) quite a few times as I rode around the  neighborhood. It didn't happen every time, but it happened often enough that I worried that maybe the bike wasn't going to work for me.

[I pause here to define "chainstay." The chainstay is the metal bar of a bicycle frame that runs parallel to the pavement between the bottom bracket (where the pedals attach) and the rear axle. The rear part of this metal bar bends outward from the wheel axle to accommodate all the gear sprockets back there, and it is this portion of the chainstay--the part that sticks out--that my heel strikes as my foot circulates around with the pedals. See photo below]

The red bar is the chainstay. Photo from http://lizardskins.com/store/products/mountain/bike-protection/standard-chainstay-protector.

So back to the heel-strike issue. I pointed out the problem to the salesperson and he suggested that I try wearing different shoes (I was wearing running shoes that have a lot of material at the heel end). That made sense, so I looked over the shop's selection of cycling shoes. Many cycling shoes have a narrower heel than my running shoes, so with a narrower heel, I might not hit the chainstay as often. Choosing a pair of shoes, I discovered that the bike shop's inventory did not include my size. I wear size 13US. This isn't surprising, as I have trouble finding a good selection of shoes at any store, but it was a little funny that the bike shop had to not only special order a bike, but also shoes, for me. They ordered a couple varieties for me and I'll drop by tomorrow to see how the shoes fit and whether they solve the heel-strike problem.

But what if the shoes don't solve the heel-strike issue? Well, I figured I should go to a different bike shop and take a second bike for a test drive. I reasoned that maybe the problem with the first bike was its design, and maybe a different bike wouldn't cause this heel-strike problem.

The salesperson at the second bike shop couldn't find a 60cm frame, either. So I hopped on a 58cm frame and took it for a test drive. I wore the same shoes as before, since I almost always wear running shoes...even when I'm not running. This second bike still caused my heel to strike the chainstay (more notably on the left side this time). So it appears I'll have this issue regardless of bike make and model. 

So I'm strongly leaning toward buying that first bike, even if the heel-strike issue is unresolved by new cycling shoes. I expect I will quickly learn to position my feet in a way that will avoid the chainstay. For instance, pointing my toes inward will cause my heels to be oriented to the outside edge of the pedal, and presumably this will be enough to avoid striking my heel on the chainstay. But will this altered foot position cause me harm?

Is there anyone out there with this "big foot" problem?

Why don't bicycle designers make a frame that fits big people?!