Looks like the stem is already as far up the steerer as it will go. If that doesn't put the bars high enough for you, there are a few BMX bars currently available with 9" rise. Most are only 7 1/2 or 8 inch high. Get the longest seat post you can find. You might not be able to get the seat up to "proper" height, but you should at least be able to get it high enough to be comfortable. Due to the popularity of freestyle, and the overgrooming of most modern BMX race tracks, there are plenty of 20" street tires available out there.

For the record, the only problem I've ever had riding BMX bikes long distance, is from me being out of shape. I'm 5'7", but I have a 32" inseam. I have no problem getting my seat up high enough to have my legs straight, with my feet on the ground, while sitting on the seat. (which is where I prefer my seat) I'm currently running a shade higher than that, but I'm not at the maximum height marked on my seat post. My bike is an older one, so my seat tube is an inch or so taller than yours.

I've never had a problem adjusting a BMX race saddle to be comfortable for riding on, especially the padded ones. Just play around with the angle, until it feels right.

With a quick release seat post clamp, you can always drop the seat, and hit some jumps on your commuter.