It appears Tsunayoshi made a quick decision with political purpose, he wanted to prevent his real mother Keisho-in's being granted Juichii (Junior First Rank) from being washed out, displaying his allegiance to the Imperial Court by carrying out Naganori's execution.
ここまで綱吉が切腹を急いだのは、長矩の処分を断行することで自らの朝廷への恭順の意思を示して綱吉生母桂昌院への従一位下賜がお流れにならないようにしようという政治的意味合いもあったようだ。