I'm not 100% sure but I do not think you will be deleted from the "black list" until you settle the payment with Softbank.
I searched with Google and found this article ( in Japanese.)
ホントは怖い携帯料金滞納。ソフトバンクを例に解説。信用情報に傷が付くことも | キャッシングのまとめ
It says that if you do not pay in time, it does damage your credit record because during the initial contract period the cost of the phone is included in the monthly payment, which is the same thing that you're making a loan from the carrier (in your case Softbank).
I cannot find out if the article was written recently or sometime ago and in the latter case whether it was updated or not, but according to the article annual interest is 14.5%.
If you failed to make payment four years ago and the amount you owe is JPY60,000, it is likely that you have to pay semething around JPY94,800 (but not JPY300,000).
If you wish to have a new contract with docomo, I think the best option is to contact Softbank and see how much you have to pay, and make the payment as early as possible before it gets bigger in amount.
Just my 2 cents.