My answer is a bit late, but I think late is better than never. I can only assume that you're using your false chords to create the roughness.
What you need to do then is to train your false chords to function independently of the vocal folds.
The problem might be that you are not able to adduct the false chords without simultaniously compressing the vocal folds, which forces you to use much more pressure than necessary. There are some exercises that help to get the right coordination (assuming you're already know the basic technique).
(1) Pick a pitch. Switch back and forth between a clean and a distorted tone. Whilst doing so, try to get both coordinations as close to each other as possible, so that you can change very fast between the two. Get a good timbre and ease in the clean tone and try to maintain that in the distorted tone. Try not to change anything, but adding the distortion. The goal is to find that magical spot where the voice flips. It's important to to this a lot in order to build the proper muscles. I'm calling this false chord pushups.
(2) Do exercise (1), but try to go with as little volume as possible with the voice, while still remaining at that tipping point.
(3) Pick a pitch and sing a sustained note with distortion. Now slowing reduce volume and breath pressure, while trying to maintain the distortion. How light can you go? You will have to adjust your coordination in order to be able to go lighter. You might have to increase or reduce the amount of distortion. Repeat for different pitches.
A final tip on this would be to learn false chords screams, because this technique teaches you to engage the false chords while keeping the vocal folds loose. However, the effort is not worth the gain if you don't actually want to use this in your singing.
Another problem could be that you're not able to engage the false chords just a little bit. The more you engage the false chords, the more difficult it is to keep the sound light higher up the range. This exercise is more advanced:
(4) Go through different pitches. For each one start with a nice clean tone and aim towards adding just a tiny touch of distortion. Your goal is to find the lowest amount of distortion possible. Then smoothly blend in more and more distortion. Finally gradually reduce it again, until you're left with the clean voice.
(5) Use a pitch and a vowel which makes is easy for you not to push to enter distortion. Keep it easy and just add a touch of distortion. Now maintain that coordination, while you progress into more difficult territory via scales or sweeps. Can you get across your passagio?
(6) Sing scales in staccato with distortion. What you want to aim for is a defined distorted tone already from the start the onset should be balanced, i.e. you should not hear breathiness or a glottal attack, or even feel tension building up. In order to do that you need to build strong muscles and a coordination that allows you to sing easy.
Yet another problem might be that your mixed voice is not evolved enough yet to support the minimum intensity that distortion definitely requires and this forces you to push. In this case, I recommend working on building your mixed voice, so you can give it a more intense, thicker sound without straining. I'm not gonna suggest how to practice this, since the internet is already full of information.
One more exercise might help:
(7) Do exercise (5), but do it on "n". Since this consonant minimizes mouth resonance, it exposes any reliance on mouth resonance and encourages you to get the proper basis laid down in the larynx. Whenever you find yourself pushing or tensing up, try again.
Admittedly, some of these exercises are very though for the casual rough singer, but they definitely worked and still do work for me. Just make sure to always work with exercises that fit your current level - the ones that are challenging, but can still be executed correctly.