"I want the light slightly harder and narrower than the Elinchrom 70 I'm actually using."
To achieve the look that you are going for "harder" (more contrast) and narrower, covering less of the subject with the direct rays of the parabola of the beauty dish, you do only two things with the 70 cm, dish that you are using now. You may need to purchase or rent a few items, that are much less expensive that buying a new beauty dish, but in learning how their use modifies light, you will greatly advance your skill of lighting.
Making the light "HARDER"
Double the distance the the light modifier is placed relative to the subject. This will have the desired effect on contrast (hardness). However it will have an undesired effect on coverage of the light, making it still broader than you desire. To maintain the same exposure settings you will need to increase the output of your strobe.
Making the cone of light "NARROWER"
To overcome the broadening of the cone of light that doubling the distance that the light is from the subject, you may first try modifying the light that is leaving the light modifier. The appropriate modifier to achieve the narrowing is a grid; there being several grid patterns, you can experiment starting with the widest honeycomb grid and progressing narrower and still narrower. Should you find that this modification of the light modifier by the addition of grids is still not getting you where you want to be in terms of restricting where light strikes the subject, then you may use flags or a gobo, that go between the light source and the subject. The utilization of the modeling light is quite helpful as you range the flags closer or further from the subject in this way restricting the light to that portion of the subject that you desire. Should you find that you dislike the abruptness of the cut off between that portion of the subject receiving light directly and the portion being partially block (receiving light that is scattered, but not from the direct rays) then the next step is to use flags that let part of the light pass through the fabric. There are various densities of flags available for this purpose.
Matthews and Westcott and two providers whose products are widely utilized for this purpose. Here's hoping that you will share some of your experiments with varying the characteristic of light and its coverage as you make progress on your creative path. I am certain that other readers will enjoy sharing with you your findings.
Good luck,
Jerry Reed