Not to mention, just eating conbini the ENTIRE time can get very unhealthy, very quick. You will need proper proteins and diet especially if you're going to have an adventurous type trip.
A lot of people are trying to tell you that your plan is far-fetched, but I would say go for it. What's the worst that could happen? Death? Major illness? Lose all your cash in the first few days and have to live on the street until you are arrested and deported and banned from the country?
Seriously, try to shorten it up a little bit (maybe knock a month off), add a little bit more cash to your budget and maybe look into a youth hostel instead of a capsule hotel (which you will literally be sick of after a week - physically ill). I know there are hostels that will give you a room for 1500-2000¥ a night.
Remember, it is all about quality, not quantity. If you do it the way you're proposing, you may end up resenting Japan for the wrong reasons.