You have some conflicting requirements here.

1) Most Specialized shoes will probably fit you if this is the brand you like best so far. Selection can be slim, so you may just have to order online. If you want stiff shoes, you need some high quality shoes, which translates to more $$. If you want a stiff shoe that is walkable and treaded so you won't slip, then you're looking at good MTB shoes, although road shoes will have bumpers on the toe and heel to minimize slipping--you just have to get the hang of it, and stopping on a steep grade could still suck.

2) Here is where you are going to be compromising stiffness and walkability. To have a shoe with 2-bolt and 3 bolt patterns, you need a road sole. However, you aren't going to be able to find carbon-soled road shoes that have the SPD plate easily. So you're looking at plastic/fiberglass soles which aren't as stiff. MTB shoes will not have the 3-bolt pattern needed for road cleat systems, so you will lose walkability by giving up MTB shoe tread.

3) Your concern is possible, but the right fitting shoe will alleviate a lot of foot discomfort. From there, you need to examine the cleat type (surface area of contact, for example) and, most importantly, cleat position.

So, you should prioritize the benefits of a road shoe with the drawbacks of switching to a road shoe without switching away from SPD at the same time. If you are sure you want to stick with SPDs, then you can get a good mountain shoe that will meet all of your other needs: stiffness, walkability, and tread against slipping. It sounds to me like you're more concerned about foot comfort than the walking factor, so I would go with a good road shoe and switch pedal systems all at the same time.