what size are you playing on the HR* i have a 7m Hr* and man its loud, but like you i also felt i needed to be louder with more edge, though i love the sound that it has. I just bought a Jody Jazz DV and man do i love it its loud but plays nice when playing softly. Although you mentioned you want to stick with hard rubber i imagine the HR* is a very well balenced mpc with enough edge and projection but is you want more you might want to check out the metal mpc's i would recommend the jody jazz dv i tried a good number of mpc not too long ago, side by side and the dv stood out the best.
Another options would be trying a moutpiece with a spoiler jody jazz makes a mpc called the classic its hard rubber and has the option of the spoiler should you want more projection and edge
check out these links...the classic is more brighter and projects more the the hr according the jody's website. check these links out!
classic mps overview:
again i own a hr and a dv, my take on this is that i want my hr rubber piece with edge and volume but i dont want it to be super bright which is why i use the hr(but this is as bright as i will go on rubber for my taste), and i use the dv for more modern stuff, this mpc is bright but still enjoyable
hope this helps!