I had no idea they were ending this program. I had a MEXT scholarship for a PhD in aerospace engineering. In my case I tried the recommendation via school first and didn't get it even though I did have a letter from a Professor. By coincidence a year later I had an internship in Japan with another Professor and with his support I got into the program via the embassy route.

Your experience mostly tracks with mine, but in my case there was a lot of interaction between Japanese and foreign students, and international journal and conference submissions were preferred. Many courses were offered in English and those that weren't, I could do homework and tests in English. Thesis had to be in English, even for Japanese students. It was a goal of the program to also help Japanese students get comfortable with international collaboration and working in English.

In my case I stayed in Japan for a decade and it was overall a very good experience.

One note about working as a student in Japan. You can work up to 28 hours a week without limitations as you noted. You can even work remotely for a foreign company, which is unique because if you have a work visa and freelance in Japan either as your main job, or a side job, your main client is supposed to be Japanese. This is a slightly grey area, your taxes are to be paid in Japan, and the company will be "operating in Japan" so be very careful about doing this by the books.