I have done the same. What I do is I first make sure I die, as to stop myself to getting a Perfect Clear which leads to an S Rank, then I do little tiny flicks of the left stick (I have the Xbox version, in case you're wondering), and that usually gets me to the first Grinding part in just above 3 1/2 minutes, which with no Rings would probably get you a B Rank.
Yep, I don't Boost either. I go back to hit enemies I missed or to pointlessly gather that last Red Star Ring. I go 'old-school' mode where I don't Homing Attack, Quick Step, Drift, Slide or Boost (Slide only is excepted where I am forced to Slide).
What I also do is I allow enemies to hit me, then I gather a Ring, then repeat for a while. I also go AFC (Away From Controller :D) with the game unpaused, so when I get back the timer is like at 17 minutes.
That has got me a D rank. Just be VERY slow and do pointless stuff