Hi Rick, I've been touring for 37 years, 14 of those with my Bike Friday New World Tourist. In Japan, using trains and ferries and sometimes planes, the folding aspect definitely makes a big difference (I used to do "rinko" cycling... bagging a full-wheel bike, too) . Bike Fridays as custom made and you can get them in Japan from the fantastic Bike Friday main representative Cycletech-IKD in Takasaki (with mail order very easy to do and a great staff who a very friendly to non-Japanese) or the Tokyo Bike Friday store Amanda Cycle, who I've heard are good, too. If you're not going to be doing huge distances and folding is the most important concern, than I recommend the Bike Friday Tikit, the Brompton (smallest folder), or the German-made Birdy BD-1. The Tikit has the best ride here. For longer distances I'd recommend the Bike Friday New World Tourist for it's better handling and touring geometry.
Small wheels have problems and pluses. Like was said they ride more harshly and are more squirrelly to handle. However, the are also much stronger than larger wheels and accelerate better. I tone down the road rattle buy using fatter tires kept at a slightly lower pressure, so the tires absorb some of the road roughness. You can easily find 20" tires at children's bike shops, which is why the Bike Friday New World Tourist has an advantage here. The others all use unusual smaller wheels.
I wouldn't recommend putting too much weight on the front rack because small-wheeled bicycles already have overly quickly front wheel handling. Keep the weight down low (as near the axels of the wheels as you can), and back. Unlike mountain bikes using the Revelate Designs and Carousel Designs bike packing bags, which have much bigger wheels and a better gyroscopic effect, small wheels will be more unstable if you keep the weight too high. So it's best to keep most of your camping gear in panniers low down in the rear. Just make sure the panniers are far enough to the rear that your heels don't hit them when you pedal.
In Japan women tend to favor the Brompton because of it's design and second to that, the Tikit. Both are easier for women to carry than the New World Tourist or BD-1, especially small women. This includes the problem of weight, but also the size for when you do things like carry the bikes down train station stairs.
Here is a site with suggestions for cycling routes in Japan. He mostly uses a Bike Friday New World Tourist recently.